Han Zhao | 赵晗

Domain generalization (DG) seeks to develop models that generalize well to unseen target domains, addressing the prevalent issue of distribution shifts in real-world applications. One line of research in DG focuses on aligning domain-level gradients and Hessians to enhance generalization. However, existing methods are computationally inefficient and the underlying principles of these approaches are not well understood. In this paper, we develop the theory of moment alignment for DG. Grounded in \textit{transfer measure}, a principled framework for quantifying generalizability between two domains, we first extend the definition of transfer measure to domain generalization that includes multiple source domains and establish a target error bound. Then, we prove that aligning derivatives across domains improves transfer measure both when the feature extractor induces an invariant optimal predictor across domains and when it does not. Notably, moment alignment provides a unifying understanding of Invariant Risk Minimization, gradient matching, and Hessian matching, three previously disconnected approaches to DG. We further connect feature moments and derivatives of the classifier head, and establish the duality between feature learning and classifier fitting. Building upon our theory, we introduce \textbf{C}losed-Form \textbf{M}oment \textbf{A}lignment (CMA), a novel DG algorithm that aligns domain-level gradients and Hessians in closed-form. Our method overcomes the computational inefficiencies of existing gradient and Hessian-based techniques by eliminating the need for repeated backpropagation or sampling-based Hessian estimation. We validate the efficacy of our approach through two sets of experiments: linear probing and full fine-tuning. CMA demonstrates superior performance in both settings compared to Empirical Risk Minimization and state-of-the-art algorithms.

Distribution matching is a core concept in machine learning, with applications in generative models, domain adaptation, and algorithmic fairness. A closely related but less explored challenge is generating a distribution that aligns with multiple underlying distributions, often with conflicting objectives, known as a Pareto optimal distribution. In this paper, we develop a general theory based on information geometry to construct the Pareto set and front for the entire exponential family under KL and inverse KL divergences. This formulation allows explicit derivation of the Pareto set and front for multivariate normal distributions, enabling applications like multiobjective variational autoencoders (MOVAEs) to generate interpolated image distributions. Experimental results on real-world images demonstrate that both algorithms can generate high-quality interpolated images across multiple distributions.

We propose a novel scaling law for general-purpose decoder-only language models (LMs) trained on multilingual data, tackling the problem of balancing languages during multilingual pretraining. A primary challenge in studying multilingual scaling is the difficulty of analyzing individual language performance due to cross-lingual transfer. To address this, we shift the focus from individual languages to language families. We introduce and validate a hypothesis that the test cross-entropy loss for each language family is determined solely by its own sampling ratio, independent of other languages in the mixture. This insight simplifies the complexity of multilingual scaling and make the analysis scalable to an arbitrary number of languages. Building on this hypothesis, we derive a power-law relationship that links performance with dataset size, model size and sampling ratios. This relationship enables us to predict performance across various combinations of the above three quantities, and derive the optimal sampling ratios at different model scales. To demonstrate the effectiveness and accuracy of our proposed scaling law, we perform a large-scale empirical study, training more than 100 models on 23 languages spanning 5 language families. Our experiments show that the optimal sampling ratios derived from small models (85M parameters) generalize effectively to models that are several orders of magnitude larger (1.2B parameters), offering a resource-efficient approach for multilingual LM training at scale.

The AI community has witnessed the emergence of various chat-style Large Language Models (LLMs) since the advent of ChatGPT. Despite significant progress in this area, evaluating these models remains a substantial challenge. The evaluations provided by humans or GPT-4 oracles are often taken as the gold standard, but they are neither automatic nor scalable. More recently, a series of (open-source) LLM-based judge models have been introduced, yet they often exhibit model-specific biases, e.g., a LLaMA-family judge favors a LLaMAfamily model. On the other hand, autoregressive evaluation metrics, which holds the potential to address the aforementioned issues, remains underexplored. Among them, likelihood-based metrics such as perplexity and negative log-likelihood (NLL) are widely adopted and has proven effective in tracking the pretraining progress of LLMs. However, they struggle to evaluate the generation capabilities of fine-tuned models due to exposure bias, a phenomenon where the distribution of the model's output gradually deviates from the ground-truth during inference. To address this key issue, in this paper, we propose a novel autoregressive metric, Normalized Discounted Cumulative Gain (NDCG), to improve the evaluation of fine-tuned LLMs. Our experimental results demonstrate that NDCG significantly outperforms likelihood-based metrics: it shows over 45% improvement in both Spearman and Kendall's tau correlation coefficients for commonsense QA tasks, and aligns more closely with GPT-4 Elo rankings for instruction-tuned models.

To embed structured knowledge within labels into feature representations, prior work (Zeng et al., 2022) proposed to use the Cophenetic Correlation Coefficient (CPCC) as a regularizer during supervised learning. This regularizer calculates pairwise Euclidean distances of class means and aligns them with the corresponding shortest path distances derived from the label hierarchy tree. However, class means may not be good representatives of the class conditional distributions, especially when they are multi-mode in nature. To address this limitation, under the CPCC framework, we propose to use the Earth Mover's Distance (EMD) to measure the pairwise distances among classes in the feature space. We show that our exact EMD method generalizes previous work, and recovers the existing algorithm when class-conditional distributions are Gaussian in the feature space. To further improve the computational efficiency of our method, we introduce the Optimal Transport-CPCC family by exploring four EMD approximation variants. Our most efficient OT-CPCC variant runs in linear time in the size of the dataset, while maintaining competitive performance across datasets and tasks. The code is available at https://github.com/uiuctml/OTCPCC.

Neural Ordinary Differential Equations (Neural ODEs or NODEs) excel at modeling continuous dynamical systems from observational data, especially when the data is irregularly sampled. However, existing training methods predominantly rely on numerical ODE solvers, which are time-consuming and prone to accumulating numerical errors over time due to autoregression. In this work, we propose VF-NODE, a novel approach based on the variational formulation (VF) to accelerate the training of NODEs. Unlike existing training methods, the proposed VF-NODEs implement a series of global integrals, thus evaluating Deep Neural Network (DNN)--based vector fields only at specific observed data points. This strategy drastically reduces the number of function evaluations (NFEs). Moreover, our method eliminates the use of autoregression, thereby reducing error accumulations for modeling dynamical systems. Nevertheless, the VF loss introduces oscillatory terms into the integrals when using the Fourier basis. We incorporate Filon's method to address this issue. To further enhance the performance for noisy and incomplete data, we employ the natural cubic spline regression to estimate a closed-form approximation. We provide a fundamental analysis of how our approach minimizes computational costs. Extensive experiments demonstrate that our approach accelerates NODE training by 10 to 1000 times compared to existing NODE-based methods, while achieving higher or comparable accuracy in dynamical systems. The code is available at https://github.com/ZhaoHongjue/VF-NODE-ICLR2025.

Recent advancements in Large Language Models (LLMs) have sparked widespread concerns about their safety. Recent work demonstrates that safety alignment of LLMs can be easily removed by fine-tuning with a few adversarially chosen instruction-following examples, i.e., fine-tuning attacks. We take a further step to understand fine-tuning attacks in multilingual LLMs. We first discover cross-lingual generalization of fine-tuning attacks: using a few adversarially chosen instruction-following examples in one language, multilingual LLMs can also be easily compromised (e.g., multilingual LLMs fail to refuse harmful prompts in other languages). Motivated by this finding, we hypothesize that safety-related information is language-agnostic and propose a new method termed Safety Information Localization (SIL) to identify the safety-related information in the model parameter space. Through SIL, we validate this hypothesis and find that only changing 20% of weight parameters in fine-tuning attacks can break safety alignment across all languages. Furthermore, we provide evidence to the alternative pathways hypothesis for why freezing safety-related parameters does not prevent fine-tuning attacks, and we demonstrate that our attack vector can still jailbreak LLMs adapted to new languages.

Model merging offers an effective strategy to combine the strengths of multiple finetuned models into a unified model that preserves the specialized capabilities of each. Existing methods merge models in a global manner, performing arithmetic operations across all model parameters. However, such global merging often leads to task interference, degrading the performance of the merged model. In this work, we introduce Localize-and-Stitch, a novel approach that merges models in a localized way. Our algorithm works in two steps: i) Localization: identify tiny (1% of the total parameters) localized regions in the finetuned models containing essential skills for the downstream tasks, and ii) Stitching: reintegrate only these essential regions back into the pretrained model for task synergy. We demonstrate that our approach effectively locates sparse regions responsible for finetuned performance, and the localized regions could be treated as compact and interpretable representations of the finetuned models (tasks). Empirically, we evaluate our method on various vision and language benchmarks, showing that it outperforms existing model merging methods under different data availability scenarios. Beyond strong empirical performance, our algorithm also facilitates model compression and preserves pretrained knowledge, enabling flexible and continual skill composition from multiple finetuned models with minimal storage and computational overhead.

How can we attribute the behaviors of machine learning models to their training data? While the classic influence function sheds light on the impact of individual samples, it often fails to capture the more complex and pronounced collective influence of a set of samples. To tackle this challenge, we study the Most Influential Subset Selection (MISS) problem, which aims to identify a subset of training samples with the greatest collective influence. We conduct a comprehensive analysis of the prevailing approaches in MISS, elucidating their strengths and weaknesses. Our findings reveal that influence-based greedy heuristics, a dominant class of algorithms in MISS, can provably fail even in linear regression. We delineate the failure modes, including the errors of influence function and the non-additive structure of the collective influence. Conversely, we demonstrate that an adaptive version of these heuristics which applies them iteratively, can effectively capture the interactions among samples and thus partially address the issues. Experiments on real-world datasets corroborate these theoretical findings, and further demonstrate that the merit of adaptivity can extend to more complex scenarios such as classification tasks and non-linear neural networks. We conclude our analysis by emphasizing the inherent trade-off between performance and computational efficiency, questioning the use of additive metrics such as the linear datamodeling score, and offering a range of discussions.

Most real-world datasets consist of a natural hierarchy between classes or an inherent label structure that is either already available or can be constructed cheaply. However, most existing representation learning methods ignore this hierarchy, treating labels as permutation invariant. Recent work [Zeng et al., 2022] proposes using this structured information explicitly, but the use of Euclidean distance may distort the underlying semantic context [Chen et al., 2013]. In this work, motivated by the advantage of hyperbolic spaces in modeling hierarchical relationships, we propose a novel approach HypStructure: a Hyperbolic Structured regularization approach to accurately embed the label hierarchy into the learned representations. HypStructure is a simple-yet-effective regularizer that consists of a hyperbolic tree-based representation loss along with a centering loss, and can be combined with any standard task loss to learn hierarchy-informed features. Extensive experiments on several large-scale vision benchmarks demonstrate the efficacy of HypStructure in reducing distortion and boosting generalization performance especially under low dimensional scenarios. For a better understanding of structured representation, we perform eigenvalue analysis that links the representation geometry to improved Out-of-Distribution (OOD) detection performance seen empirically.

Probabilistic circuits (PCs) have emerged as a powerful framework to compactly represent probability distributions for efficient and exact probabilistic inference. It has been shown that PCs with a general directed acyclic graph (DAG) structure can be understood as a mixture of exponentially (in its height) many components, each of which is a product distribution over univariate marginals. However, existing structure learning algorithms for PCs often generate tree-structured circuits or use tree-structured circuits as intermediate steps to compress them into DAG-structured circuits. This leads to the intriguing question of whether there exists an exponential gap between DAGs and trees for the PC structure. In this paper, we provide a negative answer to this conjecture by proving that, for n variables, there exists a quasi-polynomial upper bound $n^O(\log n)$ on the size of an equivalent tree computing the same probability distribution. On the other hand, we also show that given a depth restriction on the tree, there is a super-polynomial separation between tree and DAG-structured PCs. Our work takes an important step towards understanding the expressive power of tree-structured PCs, and our techniques may be of independent interest in the study of structure learning algorithms for PCs.

The performance of Transfer Learning (TL) heavily relies on effective pretraining, which demands large datasets and substantial computational resources. As a result, executing TL is often challenging for individual model developers. Federated Learning (FL) addresses these issues by facilitating collaborations among clients, expanding the dataset indirectly, distributing computational costs, and preserving privacy. However, key challenges remain unresolved. First, existing FL methods tend to optimize transferability only within local domains, neglecting the global learning domain. Second, most approaches rely on indirect transferability metrics, which do not accurately reflect the final target loss or true degree of transferability. To address these gaps, we propose two enhancements to FL. First, we introduce a client-server exchange protocol that leverages cross-client Jacobian (gradient) norms to boost transferability. Second, we increase the average Jacobian norm across clients at the server, using this as a local regularizer to reduce cross-client Jacobian variance. Our transferable federated algorithm, termed FedGTST (Federated Global Transferability via Statistics Tuning), demonstrates that increasing the average Jacobian and reducing its variance allows for tighter control of the target loss. This leads to an upper bound on the target loss in terms of the source loss and source-target domain discrepancy. Extensive experiments on datasets such as MNIST to MNIST-M and CIFAR10 to SVHN show that FedGTST outperforms relevant baselines, including FedSR. On the second dataset pair, FedGTST improves accuracy by 9.8% over FedSR and 7.6% over FedIIR when LeNet is used as the backbone.

Multiobjective optimization problems (MOPs) are prevalent in machine learning, with applications in multi-task learning, learning under fairness or robustness constraints, etc. Instead of reducing multiple objective functions into a scalar objective, MOPs aim to optimize for the so-called Pareto optimality or Pareto set learning, which involves optimizing more than one objective function simultaneously, over models with thousands / millions of parameters. Existing benchmark libraries for MOPs mainly focus on evolutionary algorithms, most of which are zeroth-order / meta-heuristic methods that do not effectively utilize higher-order information from objectives and cannot scale to large-scale models with thousands / millions of parameters. In light of the above gap, this paper introduces LibMOON, the first multiobjective optimization library that supports state-of-the-art gradient-based methods, provides a fair benchmark, and is open-sourced for the community.

Reinforcement learning from human feedback (RLHF) has emerged as the primary method for aligning large language models (LLMs) with human preferences. The RLHF process typically starts by training a reward model (RM) using human preference data. Conventional RMs are trained on pairwise responses to the same user request, with relative ratings indicating which response humans prefer. The trained RM serves as a proxy for human preferences. However, due to the black-box nature of RMs, their outputs lack interpretability, as humans cannot intuitively understand why an RM thinks a response is good or not. As RMs act as human preference proxies, we believe they should be human-interpretable to ensure that their internal decision processes are consistent with human preferences and to prevent reward hacking in LLM alignment. To build RMs with interpretable preferences, we propose a two-stage approach: i) train an Absolute-Rating Multi-Objective Reward Model (ArmoRM) with multi-dimensional absolute-rating data, each dimension corresponding to a human-interpretable objective (e.g., honesty, verbosity, safety); ii) employ a Mixture-of-Experts (MoE) strategy with a gating network that automatically selects the most suitable reward objectives based on the context. We efficiently trained an ArmoRM with Llama-3 8B and a gating network consisting of a shallow MLP on top of the ArmoRM. Our trained model, ArmoRM-Llama3-8B, obtains state-of-the-art performance on RewardBench, a benchmark evaluating RMs for language modeling. Notably, the performance of our model surpasses the LLM-as-a-judge method with GPT-4 judges by a margin, and approaches the performance of the much larger Nemotron-4 340B reward model.

Reward models (RM) capture the values and preferences of humans and play a central role in Reinforcement Learning with Human Feedback (RLHF) to align pretrained large language models (LLMs). Traditionally, training these models relies on extensive human-annotated preference data, which poses significant challenges in terms of scalability and cost. To overcome these limitations, we propose Semi-Supervised Reward Modeling (SSRM), an approach that enhances RM training using unlabeled data. Given an unlabeled dataset, SSRM involves three key iterative steps: pseudo-labeling unlabeled examples, selecting high-confidence examples through a confidence threshold, and supervised finetuning on the refined dataset. Across extensive experiments on various model configurations, we demonstrate that SSRM significantly improves reward models without incurring additional labeling costs. Notably, SSRM can achieve performance comparable to models trained entirely on labeled data of equivalent volumes. Overall, SSRM substantially reduces the dependency on large volumes of human-annotated data, thereby decreasing the overall cost and time involved in training effective reward models.

LLMs acquire a wide range of abilities during pre-training, but aligning LLMs under Reinforcement Learning with Human Feedback (RLHF) can lead to forgetting pretrained abilities, which is also known as the alignment tax. To investigate alignment tax, we conducted experiments with existing RLHF algorithms using OpenLLaMA-3B, which revealed a pronounced alignment tax in NLP tasks. Whereas, despite various techniques to mitigate forgetting, they are often at odds with the RLHF performance, leading to a trade-off between alignment performance and forgetting mitigation, leading to an alignment-forgetting trade-off. In this paper we show that model averaging, which simply interpolates between pre and post RLHF model weights, surprisingly achieves the most strongest alignment-forgetting Pareto front among a wide range of competing methods. To understand its effectiveness, we offer theoretical insights into model averaging, revealing that it enhances performance Pareto front by increasing feature diversity on the layers where tasks share overlapped feature spaces. Empirical evidence corroborates our analysis by showing the benefits of averaging low-level transformer layers. Building on the analysis and the observation that averaging different layers of the transformer leads to significantly different alignment-forgetting trade-offs, we propose Heterogeneous Model Averaging (HMA) to Heterogeneously find various combination ratios of model layers. HMA seeks to maximize the alignment performance while incurring minimal alignment tax. Moreover, we validate HMA's performance across a range of RLHF algorithms over OpenLLaMA-3B and further extend our findings to Mistral-7B which is evaluated by open-sourced preference model and GPT4.

With the development of machine learning algorithms and the increasing computational resources available, artificial intelligence has achieved great success in many application domains. However, the success of machine learning has also raised concerns about the fairness of the learned models. For instance, the learned models can perpetuate and even exacerbate the potential bias and discrimination in the training data. This issue has become a major obstacle to the deployment of machine learning systems in high-stakes domains, for example, criminal judgment, medical testing, online advertising, hiring process, and so forth. To mitigate the potential bias exhibited by machine learning models, fairness criteria can be integrated into the training process to ensure fair treatment across all demographics, but it often comes at the expense of model performance. Understanding such tradeoffs, therefore, is crucial to the design of optimal and fair algorithms. My research focuses on characterizing the inherent tradeoff between fairness and accuracy in machine learning, and developing algorithms that can achieve both fairness and optimality. In this article, I will discuss our recent work on designing post-processing algorithms for fair classification, which can be applied to a wide range of fairness criteria, including statistical parity, equal opportunity, and equalized odds, under both attribute-aware and attribute-blind settings, and is particularly suited to large-scale foundation models where retraining is expensive or even infeasible. I will also discuss the connections between our work and other related research on trustworthy machine learning, including the connections between algorithmic fairness and differential privacy as well as adversarial robustness.

In this study, we delve into the problem of self-supervised learning (SSL) utilizing the 1-Wasserstein distance on a tree structure (a.k.a., Tree-Wasserstein distance (TWD)), where TWD is defined as the L1 distance between two tree-embedded vectors. In SSL methods, the cosine similarity is often utilized as an objective function; however, it has not been well studied when utilizing the Wasserstein distance. Training the Wasserstein distance is numerically challenging. Thus, this study empirically investigates a strategy for optimizing the SSL with the Wasserstein distance and finds a stable training procedure. More specifically, we evaluate the combination of two types of TWD (total variation and ClusterTree) and several probability models, including the softmax function, the ArcFace probability model, and simplicial embedding. We propose a simple yet effective Jeffrey divergence-based regularization method to stabilize optimization. Through empirical experiments on STL10, CIFAR10, CIFAR100, and SVHN, we find that a simple combination of the softmax function and TWD can obtain significantly lower results than the standard SimCLR. Moreover, a simple combination of TWD and SimSiam fails to train the model. We find that the model performance depends on the combination of TWD and probability model, and that the Jeffrey divergence regularization helps in model training. Finally, we show that the appropriate combination of the TWD and probability model outperforms cosine similarity-based representation learning.

Unsupervised domain adaptation (UDA) adapts a model from a labeled source domain to an unlabeled target domain in a one-off way. Though widely applied, UDA faces a great challenge whenever the distribution shift between the source and the target is large. Gradual domain adaptation (GDA) mitigates this limitation by using intermediate domains to gradually adapt from the source to the target domain. In this work, we first theoretically analyze gradual self-training, a popular GDA algorithm, and provide a significantly improved generalization bound compared with Kumar et al. (2020). Our theoretical analysis leads to an interesting insight: to minimize the generalization error on the target domain, the sequence of intermediate domains should be placed uniformly along the Wasserstein geodesic between the source and target domains. The insight is particularly useful under the situation where intermediate domains are missing or scarce, which is often the case in real-world applications. Based on the insight, we propose Generative Gradual DOmain Adaptation with Optimal Transport (GOAT), an algorithmic framework that can generate intermediate domains in a data-dependent way. More concretely, we first generate intermediate domains along the Wasserstein geodesic between two given consecutive domains in a feature space, then apply gradual self-training to adapt the source-trained classifier to the target along the sequence of intermediate domains. Empirically, we demonstrate that our GOAT framework can improve the performance of standard GDA when the given intermediate domains are scarce, significantly broadening the real-world application scenarios of GDA. Our code is available at https://github.com/yifei-he/GOAT.

Multimodal learning aims to learn from data of different modalities by fusing information from heterogeneous sources. Although it is beneficial to learn from more modalities, it is often infeasible to use all available modalities under limited computational resources. Modeling with all available modalities can also be inefficient and unnecessary when information across input modalities overlaps. In this paper, we study the modality selection problem, which aims to select the most useful subset of modalities for learning under a cardinality constraint. To that end, we propose a unified theoretical framework to quantify the learning utility of modalities, and we identify dependence assumptions to flexibly model the heterogeneous nature of multimodal data, which also allows efficient algorithm design. Accordingly, we derive a greedy modality selection algorithm via submodular maximization, which selects the most useful modalities with an optimality guarantee on learning performance. We also connect marginal-contribution-based feature importance scores, such as Shapley value, from the feature selection domain to the context of modality selection, to efficiently compute the importance of individual modality. We demonstrate the efficacy of our theoretical results and modality selection algorithms on 2 synthetic and 4 real-world data sets on a diverse range of multimodal data.

Fine-grained control over large language models (LLMs) remains a significant challenge, hindering their adaptability to diverse user needs. While Reinforcement Learning from Human Feedback (RLHF) shows promise in aligning LLMs, its reliance on scalar rewards often limits its ability to capture diverse user preferences in real-world applications. To address this limitation, we introduce the Directional Preference Alignment (DPA) framework. Unlike the scalar-reward RLHF, DPA incorporates multi-objective reward modeling to represent diverse preference profiles. Additionally, DPA models user preferences as directions (i.e., unit vectors) in the reward space to achieve user-dependent preference control. Our method involves training a multi-objective reward model and then fine-tuning the LLM with a preference-conditioned variant of Rejection Sampling Finetuning (RSF), an RLHF method adopted by Llama 2. This method enjoys a better performance trade-off across various reward objectives. In comparison with the scalar-reward RLHF, DPA offers users intuitive control over LLM generation: they can arithmetically specify their desired trade-offs (e.g., more helpfulness with less verbosity). We also validate the effectiveness of DPA with real-world alignment experiments on Mistral-7B. Our method provides straightforward arithmetic control over the trade-off between helpfulness and verbosity while maintaining competitive performance with strong baselines such as Direct Preference Optimization (DPO).

This paper describes a differentially private post-processing algorithm for learning fair regressors satisfying statistical parity, addressing privacy concerns of machine learning models trained on sensitive data, as well as fairness concerns of their potential to propagate historical biases. Our algorithm can be applied to post-process any given regressor to improve fairness by remapping its outputs. It consists of three steps: first, the output distributions are estimated privately via histogram density estimation and the Laplace mechanism, then their Wasserstein barycenter is computed, and the optimal transports to the barycenter are used for post-processing to satisfy fairness. We analyze the sample complexity of our algorithm and provide fairness guarantee, revealing a trade-off between the statistical bias and variance induced from the choice of the number of bins in the histogram, in which using less bins always favors fairness at the expense of error.

Graph-based methods, pivotal for label inference over interconnected objects in many real-world applications, often encounter generalization challenges, if the graph used for model training differs significantly from the graph used for testing. This work delves into Graph Domain Adaptation (GDA) to address the unique complexities of distribution shifts over graph data, where interconnected data points experience shifts in features, labels, and in particular, connecting patterns. We propose a novel, theoretically principled method, Pairwise Alignment (Pair-Align) to counter graph structure shift by mitigating conditional structure shift (CSS) and label shift (LS). Pair-Align uses edge weights to recalibrate the influence among neighboring nodes to handle CSS and adjusts the classification loss with label weights to handle LS. Our method demonstrates superior performance in real-world applications, including node classification with region shift in social networks, and the pileup mitigation task in particle colliding experiments. For the first application, we also curate the largest dataset by far for GDA studies. Our method shows strong performance in synthetic and other existing benchmark datasets.

Multi-task learning (MTL) considers learning a joint model for multiple tasks by optimizing a convex combination of all task losses. To solve the optimization problem, existing methods use an adaptive weight updating scheme, where task weights are dynamically adjusted based on their respective losses to prioritize difficult tasks. However, these algorithms face a great challenge whenever label noise is present, in which case excessive weights tend to be assigned to noisy tasks that have relatively large Bayes optimal errors, thereby overshadowing other tasks and causing performance to drop across the board. To overcome this limitation, we propose Multi-Task Learning with Excess Risks (ExcessMTL), an excess risk-based task balancing method that updates the task weights by their distances to convergence instead. Intuitively, ExcessMTL assigns higher weights to worse-trained tasks that are further from convergence. To estimate the excess risks, we develop an efficient and accurate method with Taylor approximation. Theoretically, we show that our proposed algorithm achieves convergence guarantees and Pareto stationarity. Empirically, we evaluate our algorithm on various MTL benchmarks and demonstrate its superior performance over existing methods in the presence of label noise.

Artificial intelligence (AI) systems have the potential to revolutionize clinical practices, including improving diagnostic accuracy and surgical decision-making, while also reducing costs and manpower. However, it is important to recognize that these systems may perpetuate social inequities or demonstrate biases, such as those based on race or gender. Such biases can occur before, during, or after the development of AI models, making it critical to understand and address potential biases to enable the accurate and reliable application of AI models in clinical settings. To mitigate bias concerns during model development, we surveyed recent publications on different debiasing methods in the fields of biomedical natural language processing (NLP) or computer vision (CV). Then we discussed the methods that have been applied in the biomedical domain to address bias. We performed our literature search on PubMed, ACM digital library, and IEEE Xplore of relevant articles published between January 2018 and December 2023 using multiple combinations of keywords. We then filtered the result of 10,041 articles automatically with loose constraints, and manually inspected the abstracts of the remaining 890 articles to identify the 55 articles included in this review. Additional articles in the references are also included in this review. We discuss each method and compare its strengths and weaknesses. Finally, we review other potential methods from the general domain that could be applied to biomedicine to address bias and improve fairness. The bias of AIs in biomedicine can originate from multiple sources. Existing debiasing methods that focus on algorithms can be categorized into distributional or algorithmic.

Distribution alignment can be used to learn invariant representations with applications in fairness and robustness. Most prior works resort to adversarial alignment methods but the resulting minimax problems are unstable and challenging to optimize. Non-adversarial likelihood-based approaches either require model invertibility, impose constraints on the latent prior, or lack a generic framework for alignment. To overcome these limitations, we propose a non-adversarial VAE-based alignment method that can be applied to any model pipeline. We develop a set of alignment upper bounds (including a noisy bound) that have VAE-like objectives but with a different perspective. We carefully compare our method to prior VAE-based alignment approaches both theoretically and empirically. Finally, we demonstrate that our novel alignment losses can replace adversarial losses in standard invariant representation learning pipelines without modifying the original architectures -- thereby significantly broadening the applicability of non-adversarial alignment methods.

Among numerous linear approximation methods proposed for optimal transport (OT), tree-based methods appear to be fairly reliable, notably for language processing applications. Inspired by these tree methods, we introduce several greedy heuristics aiming to compute even faster approximations of OT. We first explicitly establish the equivalence between greedy matching and optimal transport for tree metrics, and then we show that tree greedy matching can be reduced to greedy matching on a one-dimensional line. Next, we propose two new greedy-based algorithms in one dimension: the $k$-Greedy and 1D-ICT algorithms. This novel approach provides Wasserstein approximations with accuracy similar to the original tree methods on text datasets while being faster in practice. Finally, these algorithms are applicable beyond tree approximations: using sliced projections of the original data still provides fairly good accuracy while eliminating the need for embedding the data in a fixed and rigid tree structure. This property makes these approaches even more versatile than the original tree OT methods.

This paper introduces the Fair Fairness Benchmark (\textsf{FFB}), a benchmarking framework for in-processing group fairness methods. Ensuring fairness in machine learning is critical for ethical and legal compliance. However, there exist challenges in comparing and developing of fairness methods due to inconsistencies in experimental settings, lack of accessible algorithmic implementations, and limited extensibility of current fairness packages and tools. To address these issues, we introduce an open-source, standardized benchmark for evaluating in-processing group fairness methods and provide a comprehensive analysis of state-of-the-art methods to ensure different notions of group fairness. This work offers the following key contributions: the provision of flexible, extensible, minimalistic, and research-oriented open-source code; the establishment of unified fairness method benchmarking pipelines; and extensive benchmarking, which yields key insights from 45,079 experiments. We believe our work will significantly facilitate the growth and development of the fairness research community.

We present the workflow of Online Iterative Reinforcement Learning from Human Feedback (RLHF) in this technical report, which is widely reported to outperform its offline counterpart by a large margin in the recent large language model (LLM) literature. However, existing open-source RLHF projects are still largely confined to the offline learning setting. In this technical report, we aim to fill in this gap and provide a detailed recipe that is easy to reproduce for online iterative RLHF. In particular, since online human feedback is usually infeasible for open-source communities with limited resources, we start by constructing preference models using a diverse set of open-source datasets and use the constructed proxy preference model to approximate human feedback. Then, we discuss the theoretical insights and algorithmic principles behind online iterative RLHF, followed by a detailed practical implementation. Our trained LLM, \texttt{SFR-Iterative-DPO-LLaMA-3-8B-R}, achieves impressive performance on LLM chatbot benchmarks, including AlpacaEval-2, Arena-Hard, and MT-Bench, as well as other academic benchmarks such as HumanEval and TruthfulQA. We have shown that supervised fine-tuning (SFT) and iterative RLHF can obtain state-of-the-art performance with fully open-source datasets. Further, we have made our models, curated datasets, and comprehensive step-by-step code guidebooks publicly available. Please refer to \url{https://github.com/RLHFlow/RLHF-Reward-Modeling} and \url{https://github.com/RLHFlow/Online-RLHF} for more detailed information.

Real-world applications of machine learning models often confront data distribution shifts, wherein discrepancies exist between the training and test data distributions. In the common multi-domain multi-class setup, as the number of classes and domains scales up, it becomes infeasible to gather training data for every domain-class combination. This challenge naturally leads the quest for models with Compositional Generalization (CG) ability, where models can generalize to unseen domain-class combinations. To delve into the CG challenge, we develop CG-Bench, a suite of CG benchmarks derived from existing real-world image datasets, and observe that the prevalent pretraining-finetuning paradigm on foundational models, such as CLIP and DINOv2, struggles with the challenge. To address this challenge, we propose Compositional Feature Alignment (CFA), a simple two-stage finetuning technique that i) learns two orthogonal linear heads on a pretrained encoder with respect to class and domain labels, and ii) fine-tunes the encoder with the newly learned head frozen. We theoretically and empirically justify that CFA encourages compositional feature learning of pretrained models. We further conduct extensive experiments on CG-Bench for CLIP and DINOv2, two powerful pretrained vision foundation models. Experiment results show that CFA outperforms common finetuning techniques in compositional generalization, corroborating CFA's efficacy in compositional feature learning.

Out-of-distribution (OOD) detection seeks to identify test samples that deviate from the training data, which is critical to ensuring the safety and reliability of machine learning (ML) systems. While a plethora of methods have been developed to detect uni-modal OOD samples, only a few have focused on multi-modal OOD detection. Current contrastive learning-based methods primarily address multi-modal OOD detection in a scenario where an image is not related to the class labels in training data. However, ML systems in the real-world applications may encounter a broader spectrum of anomalies caused by different factors like systematic errors in labeling, environmental changes, and sensor malfunctions. Hence, we propose a new method to be able to simultaneously detect anomalies from multiple different OOD scenarios, arising from fine-grained image features and textual descriptions, instead of large categorical information. To achieve this goal, we propose a general-purpose weakly-supervised OOD detection framework, called WOOD, that combines a binary classifier and a contrastive learning module to reap the benefits of both. In order to better distinguish in-distribution (ID) samples from OOD ones, we employ the Hinge loss to constrain the similarity of their latent representations. Moreover, we devise a new scoring metric that fuses predictions from both the binary classifier and contrastive learning to enhance OOD detection. Extensive experimental results on multiple benchmarks demonstrate that the proposed WOOD significantly outperforms the state-of-the-art methods for multi-modal OOD detection. Importantly, our approach can achieve superior detection performance in a variety of OOD scenarios.

One of the common approaches for personalizing federated learning is fine-tuning the global model for each local client. While this addresses some issues of statistical heterogeneity, we find that such personalization methods are vulnerable to spurious features at local agents, leading to reduced generalization performance. This work considers a setup where spurious features correlate with the label in each client's training environment, and the mixture of multiple training environments (i.e., the global environment) diminishes the spurious correlations. In other words, while the global federated learning model trained over the global environment suffers less from spurious features, the local fine-tuning step may lead to personalized models vulnerable to spurious correlations. In light of this practical and pressing challenge, we propose a novel strategy to mitigate the effect of spurious features during personalization by maintaining the adversarial transferability between the global and personalized models. Empirical results on object and action recognition tasks show that our proposed approach bounds personalized models from further exploiting spurious features while preserving the benefit of enhanced accuracy from fine-tuning.

Linear scalarization, i.e., combining all loss functions by a weighted sum, has been the default choice in the literature of multi-task learning (MTL) since its inception. In recent years, there is a surge of interest in developing Specialized Multi-Task Optimizers (SMTOs) that treat MTL as a multi-objective optimization problem. However, it remains open whether there is a fundamental advantage of SMTOs over scalarization. In fact, heated debates exist in the community comparing these two types of algorithms, mostly from an empirical perspective. To approach the above question, in this paper, we revisit scalarization from a theoretical perspective. We focus on linear MTL models and study whether scalarization is capable of fully exploring the Pareto front. Our findings reveal that, in contrast to recent works that claimed empirical advantages of scalarization, scalarization is inherently incapable of full exploration, especially for those Pareto optimal solutions that strike the balanced trade-offs between multiple tasks. More concretely, when the model is under-parametrized, we reveal a multi-surface structure of the feasible region and identify necessary and sufficient conditions for full exploration. This leads to the conclusion that scalarization is in general incapable of tracing out the Pareto front. Our theoretical results partially answer the open questions in Xin et al. (2021), and provide a more intuitive explanation on why scalarization fails beyond non-convexity. We additionally perform experiments on a real-world dataset using both scalarization and state-of-the-art SMTOs. The experimental results not only corroborate our theoretical findings, but also unveil the potential of SMTOs in finding balanced solutions, which cannot be achieved by scalarization.

Graph Neural Networks (GNNs) are a powerful class of machine learning models with applications in recommender systems, drug discovery, social network analysis, and computer vision. One challenge with their implementation is that GNNs often take large-scale graphs as inputs, which imposes significant computational/storage costs in the training and testing phases. In particular, the message passing operations of a GNN require multiplication of the graph adjacency matrix A ∈\R^n \times n and the data matrix X ∈\R^n \times d, and the O(n^2 d) time complexity can be prohibitive for large n. Thus, a natural question is whether it is possible to perform the GNN operations in (quasi-)linear time by avoiding the full computation of A X. To study this question, we consider the setting of a regression task on a two-layer Linear Graph Convolutional Network (GCN). We develop an efficient training algorithm based on (1) performing node subsampling, (2) estimating the leverage scores of A X based on the subsampled graph, and (3) performing leverage score sampling on A X. We show that our proposed scheme learns the regression model observing only O(nd\eps^-2\log n) entries of A in time O(nd^2 \eps^-2\log n), with the guarantee that the learned weights deviate by at most εunder the \ell_2 norm from the model learned using the entire adjacency matrix A. We present empirical results for regression problems on two real-world graphs and show that our algorithm significantly outperforms other baseline sampling strategies that exploit the same number of observations.

Domain adaptation aims to transfer the knowledge acquired by models trained on (data-rich) source domains to (low-resource) target domains, for which a popular method is invariant representation learning. While they have been studied extensively for classification and regression problems, how they apply to ranking problems, where the data and metrics have a list structure, is not well understood. Theoretically, we establish a domain adaptation generalization bound for ranking under listwise metrics such as MRR and NDCG. The bound suggests an adaptation method via learning list-level domain-invariant feature representations, whose benefits are empirically demonstrated by unsupervised domain adaptation experiments on real-world ranking tasks, including passage reranking. A key message is that for domain adaptation, the representations should be analyzed at the same level at which the metric is computed, as we show that learning invariant representations at the list level is most effective for adaptation on ranking problems.

Compared to model-free reinforcement learning (RL), model-based RL is often more sample efficient by leveraging a learned dynamics model to help decision-making. However, the learned model is usually not perfectly accurate and the error will compound in multi-step predictions, which can lead to poor asymptotic performance. In this paper, we first derive an upper bound of the return discrepancy between the real dynamics and the learned model, which reveals the fundamental problem of distribution shift between simulated data and real data. Inspired by the theoretical analysis, we propose an adaptation augmented model-based policy optimization (AMPO) framework to address the distribution shift problem from the perspectives of feature learning and instance re-weighting, respectively. Specifically, the feature-based variant, namely FAMPO, introduces unsupervised model adaptation to minimize the integral probability metric (IPM) between feature distributions from real and simulated data, while the instance-based variant, termed as IAMPO, utilizes importance sampling to re-weight the real samples used to train the model. Besides model learning, we also investigate how to improve policy optimization in the model usage phase by selecting simulated samples with different probabilities according to their uncertainty. Extensive experiments on challenging continuous control tasks show that FAMPO and IAMPO, coupled with our model usage technique, achieve superior performance against baselines, which demonstrates the effectiveness of the proposed methods.

How can we learn effective node representations on textual graphs? Graph Neural Networks (GNNs) that use Language Models (LMs) to encode textual information of graphs achieve state-of-the-art performance in many node classification tasks. Yet, combining GNNs with LMs has not been widely explored for practical deployments due to its scalability issues. In this work, we tackle this challenge by developing a Graph-Aware Distillation framework (GRAD) to encode graph structures into an LM for graph-free, fast inference. Different from conventional knowledge distillation, GRAD jointly optimizes a GNN teacher and a graph-free student over the graph's nodes via a shared LM. This encourages the graph-free student to exploit graph information encoded by the GNN teacher while at the same time, enables the GNN teacher to better leverage textual information from unlabeled nodes. As a result, the teacher and the student models learn from each other to improve their overall performance. Experiments in eight node classification benchmarks in both transductive and inductive settings showcase GRAD's superiority over existing distillation approaches for textual graphs.

Fairness in automated decision-making systems has gained increasing attention as their applications expand to real-world high-stakes domains. To facilitate the design of fair ML systems, it is essential to understand the potential trade-offs between fairness and predictive power, and the construction of the optimal predictor under a given fairness constraint. In this paper, for general classification problems under the group fairness criterion of demographic parity (DP), we precisely characterize the trade-off between DP and classification accuracy, referred to as the minimum cost of fairness. Our insight comes from the key observation that finding the optimal fair classifier is equivalent to solving a Wasserstein-barycenter problem under $\ell_1$-norm restricted to the vertices of the probability simplex. Inspired by our characterization, we provide a construction of an optimal fair classifier achieving this minimum cost via the composition of the Bayes regressor and optimal transports from its output distributions to the barycenter. Our construction naturally leads to an algorithm for post-processing any pre-trained predictor to satisfy DP fairness, complemented with finite sample guarantees. Experiments on real-world datasets verify and demonstrate the effectiveness of our approaches.

While it has long been empirically observed that adversarial robustness may be at odds with standard accuracy and may have further disparate impacts on different classes, it remains an open question to what extent such observations hold and how the class imbalance plays a role within. In this paper, we attempt to understand this question of accuracy disparity by taking a closer look at linear classifiers under a Gaussian mixture model. We decompose the impact of adversarial robustness into two parts: an inherent effect that will degrade the standard accuracy on all classes, and the other caused by the class imbalance ratio, which will increase the accuracy disparity compared to standard training. Furthermore, we also extend our model to the general family of stable distributions. We demonstrate that while the constraint of adversarial robustness consistently degrades the standard accuracy in the balanced class setting, the class imbalance ratio plays a fundamentally different role in accuracy disparity compared to the Gaussian case, due to the heavy tail of the stable distribution. We additionally perform experiments on both synthetic and real-world datasets. The empirical results not only corroborate our theoretical findings, but also suggest that the implications may extend to nonlinear models over real-world datasets.

In many real-world applications, graph-structured data used for training and testing have differences in distribution, such as in high energy physics (HEP) where simulation data used for training may not match real experiments. Graph domain adaptation (GDA) is a method used to address these differences. However, current GDA primarily works by aligning the distributions of node representations output by a single graph neural network encoder shared across the two domains, which may often yield sub-optimal solutions. This work examines different impacts of distribution shifts caused by either graph structure or node attributes and identifies a new type of shift, named conditional structure shift, which current GDA approaches are provably sub-optimal to deal with. A novel approach, called structural reweighting (StruRW), is proposed to address this issue and is tested on synthetic graphs, four benchmark datasets, and a new application in HEP. StruRW has shown significant performance improvement over the baselines in the settings with large graph structure shifts, and reasonable performance improvement when node attribute shifts dominate.

Contrastive loss has been increasingly used in learning representations from multiple modalities. In the limit, the nature of the contrastive loss encourages modalities to exactly match each other in the latent space. Yet it remains an open question how the modality alignment affects the downstream task performance. In this paper, based on an information-theoretic argument, we first prove that exact modality alignment is sub-optimal in general for downstream prediction tasks. Hence we advocate that the key of better performance lies in meaningful latent modality structures instead of perfect modality alignment. To this end, we propose three general approaches to construct latent modality structures. Specifically, we design 1) a deep feature separation loss for intra-modality regularization; 2) a Brownian-bridge loss for inter-modality regularization; and 3) a geometric consistency loss for both intra- and inter-modality regularization. Extensive experiments are conducted on two popular multi-modal representation learning frameworks: the CLIP-based two-tower model and the ALBEF-based fusion model. We test our model on a variety of tasks including zero/few-shot image classification, image-text retrieval, visual question answering, visual reasoning, and visual entailment. Our method achieves consistent improvements over existing methods, demonstrating the effectiveness and generalizability of our proposed approach on latent modality structure regularization.

Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute. However, the exact tradeoff between fairness and accuracy with a real-valued target is not entirely clear. In this paper, we characterize the inherent tradeoff between statistical parity and accuracy in the regression setting by providing a lower bound on the error of any attribute-blind fair regressor. Our lower bound is sharp, algorithm-independent, and admits a simple interpretation: when the moments of the target differ between groups, any fair algorithm has to make an error on at least one of the groups. We further extend this result to give a lower bound on the joint error of any (approximately) fair algorithm, using the Wasserstein distance to measure the quality of the approximation. With our novel lower bound, we also show that the price paid by a fair regressor that does not take the protected attribute as input is less than that of a fair regressor with explicit access to the protected attribute. On the upside, we establish the first connection between individual fairness, accuracy parity, and the Wasserstein distance by showing that if a regressor is individually fair, it also approximately verifies the accuracy parity, where the gap is again given by the Wasserstein distance between the two groups. Inspired by our theoretical results, we develop a practical algorithm for fair regression through the lens of representation learning, and conduct experiments on a real-world dataset to corroborate our findings.

Existing models for learning representations in supervised classification problems are permutation invariant with respect to class labels. However, structured knowledge about the classes, such as hierarchical label structures, widely exists in many real-world datasets, e.g., the ImageNet and CIFAR benchmarks. How to learn representations that can preserve such structures among the classes remains an open problem. To approach this problem, given a tree of class hierarchy, we first define a tree metric between any pair of nodes in the tree to be the length of the shortest path connecting them. We then provide a method to learn the hierarchical relationship of class labels by approximately embedding the tree metric in the Euclidean space of features. More concretely, during supervised training, we propose to use the Cophenetic Correlation Coefficient (CPCC) as a regularizer for the cross-entropy loss to correlate the tree metric of classes and the Euclidean distance in the class-conditioned representations. Our proposed regularizer is computationally lightweight and easy to implement. Empirically, we demonstrate that this approach can help to learn more interpretable representations due to the preservation of the tree metric, and leads to better generalization in-distribution as well as under sub-population shifts over multiple datasets.

Computing the dominant eigenvectors of a matrix $A$ has many applications, such as principal component analysis, spectral embedding, and PageRank. However, in general, this task relies on the complete knowledge of the matrix $A$, which can be too large to store or even infeasible to observe in many applications, e.g., large-scale social networks. Thus, a natural question is how to accurately estimate the eigenvectors of $A$ when only partial observations can be made by sampling entries from $A$. To this end, we propose the Adaptive Power Method (\apmnospace), a variant of the well-known power method. At each power iteration, \apm adaptively selects a subset of the entries of $A$ to observe based on the current estimate of the top eigenvector. We show that \apm can estimate the dominant eigenvector(s) of $A$ with squared error at most $\epsilon$ by observing roughly $O(n\eps^{-2} \log^2 (n/\eps))$ entries of an $n\times n$ matrix. We present empirical results for the problem of eigenvector centrality computation on two real-world graphs and show that \apm significantly outperforms a non-adaptive estimation algorithm using the same number of observations. Furthermore, in the context of eigenvector centrality, \apm can also adaptively allocate the observation budget to selectively refine the estimate of nodes with high centrality scores in the graph.

Federated adversary domain adaptation is a unique distributed minimax training task due to the heterogeneous data among different local clients, where each client only sees a subset of the data that merely belongs to either the source or target domain. Despite the extensive research in distributed minimax optimization, existing communication efficient solvers that exploit multiple steps of the local update are still not able to generate satisfactory solutions for federated adversarial domain adaptation because of the gradient divergence issue among clients. To tackle this problem, we propose a distributed minimax optimizer, referred to as FedMM, by introducing dual variables to bridge the gradient gap among clients. This algorithm is effective even in the extreme case where each client has different label classes and some clients only have unlabeled data. We prove that FedMM admits benign convergence to a stationary point under domain-shifted unlabeled data. On a variety of benchmark datasets, extensive experiments show that FedMM consistently achieves both better communication savings and significant accuracy improvements over existing federated optimizers based on the stochastic gradient descent ascent (SGDA) algorithm. When training from scratch, for example, it outperforms other SGDA based federated average methods by around 20% in accuracy over the same communication rounds; and it consistently outperforms when training from pre-trained models.

Domain generalization aims to learn a model over multiple training environments to generalize to unseen environments. Recently, \cite{wang2022provable} proposed Invariant-feature Subspace Recovery (ISR), a domain generalization algorithm that uses the means of class-conditional data distributions to provably identify the invariant-feature subspace under a given causal model. However, due to the specific assumptions of the causal model, the original ISR algorithm is conditioned on a single class only, without utilizing information from the rest of the classes. In this work, we consider the setting of multi-class classification under a more general causal model, and propose an extension of the ISR algorithm, called ISR-Multiclass. This proposed algorithm can provably recover the invariant-feature subspace with $\lceil d_{spu}/k \rceil + 1$ environments, where $d_{spu}$ is the number of spurious features and $k$ is the number of classes. Empirically, we first examine ISR-Multiclass in a synthetic dataset, and demonstrate its superiority over the original ISR in the multi-class setting. Furthermore, we conduct experiments in Multiclass Coloured MNIST, a semi-synthetic dataset with strong spurious correlations, and show that ISR-Multiclass can significantly improve the robustness of neural nets trained by various methods (e.g., ERM and IRM) against spurious correlations.

The phenomenon of data distribution evolving over time has been observed in a range of applications, calling for the need for adaptive learning algorithms. We thus study the problem of supervised gradual domain adaptation, where labeled data from shifting distributions are available to the learner along the trajectory, and we aim to learn a classifier on a target data distribution of interest. Under this setting, we provide the first generalization upper bound on the learning error under mild assumptions. Our results are algorithm agnostic, general for a range of loss functions, and only depend linearly on the averaged learning error across the trajectory. This shows significant improvement compared to the previous upper bound for unsupervised gradual domain adaptation, where the learning error on the target domain depends exponentially on the initial error on the source domain. Compared with the offline setting of learning from multiple domains, our results also suggest the potential benefits of the temporal structure among different domains in adapting to the target one. Empirically, our theoretical results imply that learning proper representations across the domains will effectively mitigate learning errors. Motivated by these theoretical insights, we propose a min-max learning objective to learn the representation and classifier simultaneously. Experimental results on both semi-synthetic and large-scale real datasets corroborate our findings and demonstrate the effectiveness of our objectives.

A wide range of machine learning applications such as privacy-preserving learning, algorithmic fairness, and domain adaptation/generalization among others, involve learning \emph{invariant representations} of the data that aim to achieve two competing goals: (a) maximize information or accuracy with respect to a target response, and (b) maximize invariance or independence with respect to a set of protected features (e.g.\ for fairness, privacy, etc). Despite their wide applicability, theoretical understanding of the optimal tradeoffs --- with respect to accuracy, and invariance --- achievable by invariant representations is still severely lacking. In this paper, we provide an information theoretic analysis of such tradeoffs under both classification and regression settings. More precisely, we provide a geometric characterization of the accuracy and invariance achievable by any representation of the data; we term this feasible region the information plane. We provide an inner bound for this feasible region for the classification case, and an exact characterization for the regression case, which allows us to either bound or exactly characterize the Pareto optimal frontier between accuracy and invariance. Although our contributions are mainly theoretical, a key practical application of our results is in certifying the potential sub-optimality of any given representation learning algorithm for either classification or regression tasks. Our results shed new light on the fundamental interplay between accuracy and invariance, and may be useful in guiding the design of future representation learning algorithms.

Contrastive representation learning has gained much attention due to its superior performance in learning representations from both image and sequential data. However, the learned representations could potentially lead to performance disparities in downstream tasks, such as increased silencing of underrepresented groups in toxicity comment classification. In light of this challenge, in this work, we study learning fair representations that satisfy a notion of fairness known as equalized odds for text classification via contrastive learning. Specifically, we first theoretically analyze the connections between learning representations with a fairness constraint and \emph{conditional supervised contrastive objectives}, and then propose to use conditional supervised contrastive objectives to learn fair representations for text classification. We conduct experiments on two text datasets to demonstrate the effectiveness of our approaches in balancing the trade-offs between task performance and bias mitigation among existing baselines for text classification. Furthermore, we also show that the proposed methods are stable in different hyperparameter settings.

Generative Adversarial Networks (GANs) have been widely applied in modeling diverse image distributions. However, despite its impressive applications, the structure of the latent space in GANs largely remains as a black-box, leaving its controllable generation an open problem, especially when spurious correlations between different semantic attributes exist in the image distributions. To address this problem, previous methods typically learn linear directions or individual channels that control semantic attributes in the image space. However, they often suffer from imperfect disentanglement, or are unable to obtain multi-directional controls. In this work, in light of the above challenges, we propose a novel approach that discovers nonlinear controls, which enables multi-directional manipulation as well as effective disentanglement, based on gradient information in the learned GAN latent space. More specifically, we first learn interpolation directions by following the gradients from classification networks trained separately on the attributes, and then navigate the latent space by exclusively controlling channels activated for the target attribute in the learned directions. Empirically, with small training data, our approach is able to gain fine-grained controls over a diverse set of bi-directional and multi-directional attributes, and we showcase its ability to achieve disentanglement significantly better than state-of-the-art methods both qualitatively and quantitatively.

Multimodal learning considers learning from multi-modality data, aiming to fuse heterogeneous sources of information. However, it is not always feasible to leverage all available modalities due to memory constraints. Further, training on all the modalities may be inefficient when redundant information exists within data, such as different subsets of modalities providing similar performance. In light of these challenges, we study modality selection, intending to efficiently select the most informative and complementary modalities under certain computational constraints. We formulate a theoretical framework for optimizing modality selection in multimodal learning and introduce a utility measure to quantify the benefit of selecting a modality. For this optimization problem, we present efficient algorithms when the utility measure exhibits monotonicity and approximate submodularity. We also establish a novel correspondence between the utility measure and existing marginal contribution scores based on the Shapely value. Last, we demonstrate the efficacy of our algorithm on synthetic (Patch-MNIST) and real-world (PEMS-SF Traffic) datasets.

The vast majority of existing algorithms for unsupervised domain adaptation (UDA) focus on adapting from a labeled source domain to an unlabeled target domain directly in a one-off way. Gradual domain adaptation (GDA), on the other hand, assumes a path of ($T\mathrm{-}1$) unlabeled intermediate domains bridging the source and the target, and aims to provide better generalization on the target domain by leveraging the intermediate ones. Under certain assumptions, \citet{kumar2020understanding} proposed a simple algorithm, \textit{gradual self-training}, along with a generalization bound in the order of $e^{\mathcal O(T)}(\eps_0 \mathrm{+}\mathcal O\bigl(\sqrt {\frac{\log T}{n}}\bigr) \bigr)$ for the target domain error, where $\eps_0$ is the source domain error and $n$ is the data size of each domain. Due to the exponential factor, this upper bound becomes vacuous when $T$ is only moderately large. In this work, we analyze gradual self-training under more general and relaxed assumptions, and prove a significantly improved generalization bound as $\eps_0\mathrm{+}\widetilde{\mathcal O}\bigl(T\Delta \mathrm{+} \frac{T}{\sqrt{n}} \mathrm{+} \frac{1}{\sqrt{nT}}\bigr)$, where $\Delta$ is the average distributional distance between consecutive domains. Compared with the existing bound with an \emph{exponential} dependency on $T$ as a \textit{multiplicative} factor, our bound only depends on $T$ \emph{linearly and additively}. Perhaps more interestingly, our result implies the existence of an optimal choice of $T$ that minimizes the generalization error, and it also naturally suggests an optimal way to construct the path of intermediate domains so as to minimize the accumulative path length $T\Delta$ between the source and the target. To corroborate the implications of our theory, we examine gradual self-training on multiple semi-synthetic and real datasets, which confirms our findings. We believe our insights provide a path forward towards the design of future GDA algorithms.

Domain generalization asks for models trained on a set of training environments to perform well on unseen test environments. Recently, a series of algorithms such as Invariant Risk Minimization (IRM) has been proposed for domain generalization. However, Rosenfeld et al. (2021) shows that in a simple linear data model, even if non-convexity issues are ignored, IRM and its extensions cannot generalize to unseen environments with less than ds+1 training environments, where ds is the dimension of the spurious-feature subspace. In this paper, we propose to achieve domain generalization with Invariant-feature Subspace Recovery (ISR). Our first algorithm, ISR-Mean, can identify the subspace spanned by invariant features from the first-order moments of the class-conditional distributions, and achieve provable domain generalization with ds+1 training environments under the data model of Rosenfeld et al. (2021). Our second algorithm, ISR-Cov, further reduces the required number of training environments to O(1) using the information of second-order moments. Notably, unlike IRM, our algorithms bypass non-convexity issues and enjoy global convergence guarantees. Empirically, our ISRs can obtain superior performance compared with IRM on synthetic benchmarks. In addition, on three real-world image and text datasets, we show that ISR-Mean can be used as a simple yet effective post-processing method to increase the worst-case accuracy of trained models against spurious correlations and group shifts.

The Controllable Variational Autoencoder (ControlVAE) combines automatic control theory with the basic VAE model to manipulate the KL-divergence for overcoming posterior collapse and learning disentangled representations. It has shown success in a variety of applications, such as image generation, disentangled representation learning, and language modeling. However, when it comes to disentangled representation learning, ControlVAE does not delve into the rationale behind it. The goal of this paper is to develop a deeper understanding of ControlVAE in learning disentangled representations, including the choice of a desired KL-divergence (i.e, set point), and its stability during training. We first fundamentally explain its ability to disentangle latent variables from an information bottleneck perspective. We show that KL-divergence is an upper bound of the variational information bottleneck. By controlling the KL-divergence gradually from a small value to a target value, ControlVAE can disentangle the latent factors one by one. Based on this finding, we propose a new DynamicVAE that leverages a modified incremental PI (proportional-integral) controller, a variant of the proportional-integral-derivative (PID) algorithm, and employs a moving average as well as a hybrid annealing method to evolve the value of KL-divergence smoothly in a tightly controlled fashion. In addition, we analytically derive a lower bound of the set point for disentangling. We then theoretically prove the stability of the proposed approach. Evaluation results on multiple benchmark datasets demonstrate that DynamicVAE achieves a good trade-off between the disentanglement and reconstruction quality. We also discover that it can separate disentangled representation learning and reconstruction via manipulating the desired KL-divergence.

Recent advances in neural modeling have produced deep multilingual language models capable of extracting cross-lingual knowledge from unparallel texts, evidenced by their decent zero-shot transfer performance. While studies have attributed this success to cross-lingually shared representations, quantitative analyses are sparse. Towards a better understanding of the role of multilingual representations, in this work, we first make the following observations through empirical analysis: (1) invariance of the feature representations strongly correlates with transfer performance, and (2) distributional shift in class priors between data in the source and target languages negatively affects performance -- an issue that is largely overlooked in prior work. Based on our findings, we propose an unsupervised cross-lingual learning method, called importance-weighted domain alignment (IWDA), that performs representation alignment, prior shift estimation, and correction. Experiment results demonstrate its superiority under large prior shifts. In addition, our method delivers further performance gains when combined with existing semi-supervised learning techniques.

Conditional contrastive learning frameworks consider the conditional sampling procedure that constructs positive or negative data pairs conditioned on specific variables. Fair contrastive learning constructs negative pairs, for example, from the same gender (conditioning on sensitive information), which in turn reduces undesirable information from the learned representations; weakly supervised contrastive learning constructs positive pairs with similar annotative attributes (conditioning on auxiliary information), which in turn are incorporated into the representations. Although conditional contrastive learning enables many applications, the conditional sampling procedure can be challenging if we cannot obtain sufficient data pairs for some values of the conditioning variable. This paper presents Conditional Contrastive Learning with Kernel (CCL-K) that converts existing conditional contrastive objectives into alternative forms that mitigate the insufficient data problem. Instead of sampling data according to the value of the conditioning variable, CCLK uses the Kernel Conditional Embedding Operator that samples data from all available data and assigns weights to each sampled data given the kernel similarity between the values of the conditioning variable. We conduct experiments using weakly supervised, fair, and hard negatives contrastive learning, showing CCL-K outperforms state-of-the-art baselines.

Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute. However, the exact tradeoff between fairness and accuracy is not entirely clear, even for the basic paradigm of classification problems. In this paper, we characterize an inherent tradeoff between statistical parity and accuracy in the classification setting by providing a lower bound on the sum of group-wise errors of any fair classifiers. Our impossibility theorem could be interpreted as a certain uncertainty principle in fairness: if the base rates differ among groups, then any fair classifier satisfying statistical parity has to incur a large error on at least one of the groups. We further extend this result to give a lower bound on the joint error of any (approximately) fair classifiers, from the perspective of learning fair representations. To show that our lower bound is tight, assuming oracle access to Bayes (potentially unfair) classifiers, we also construct an algorithm that returns a randomized classifier which is both optimal (in terms of accuracy) and fair. Interestingly, when the protected attribute can take more than two values, an extension of this lower bound does not admit an analytic solution. Nevertheless, in this case, we show that the lower bound can be efficiently computed by solving a linear program, which we term as the TV-Barycenter problem, a barycenter problem under the TV-distance. On the upside, we prove that if the group-wise Bayes optimal classifiers are close, then learning fair representations leads to an alternative notion of fairness, known as the accuracy parity, which states that the error rates are close between groups. Finally, we also conduct experiments on real-world datasets to confirm our theoretical findings.

Algorithmic decisions made by machine learning models in high-stakes domains may have lasting impacts over time. Unfortunately, naive applications of standard fairness criterion in static settings over temporal domains may lead to delayed and adverse effects. To understand the dynamics of performance disparity, we study a fairness problem in Markov decision processes (MDPs). Specifically, we propose return parity, a fairness notion that requires MDPs from different demographic groups that share the same state and action spaces to achieve approximately the same expected time-discounted rewards. We first provide a decomposition theorem for return disparity, which decomposes the return disparity of any two MDPs into the distance between group-wise reward functions, the discrepancy of group policies, and the discrepancy between state visitation distributions induced by the group policies. Motivated by our decomposition theorem, we propose algorithms to mitigate return disparity via learning a shared group policy with state visitation distributional alignment using integral probability metrics. We conduct experiments to corroborate our results, showing that the proposed algorithm can successfully close the disparity gap while maintaining the performance of policies on two real-world recommender system benchmark datasets.

Models trained with offline data often suffer from continual distribution shifts and expensive labeling in changing environments. This calls for a new online learning paradigm where the learner can continually adapt to changing environments with limited labels. In this paper, we propose a new online setting -- Online Active Continual Adaptation, where the learner aims to continually adapt to changing distributions using both unlabeled samples and active queries of limited labels. To this end, we propose Online Self-Adaptive Mirror Descent (OSAMD), which adopts an online teacher-student structure to enable online self-training from unlabeled data, and a margin-based criterion that decides whether to query the labels to track changing distributions. Theoretically, we show that, in the separable case, OSAMD has an $O({T}^{1/2})$ dynamic regret bound under mild assumptions, which is even tighter than the lower bound $\Omega(T^{2/3})$ of traditional online learning with full labels. In the general case, we show a regret bound of $O({\alpha^*}^{1/3} {T}^{2/3} + \alpha^* T)$, where $\alpha^*$ denotes the separability of domains and is usually small. Our theoretical results show that OSAMD can fast adapt to changing environments with active queries. Empirically, we demonstrate that OSAMD achieves favorable regrets under changing environments with limited labels on both simulated and real-world data, which corroborates our theoretical findings.

Invariant risk minimization (IRM) has recently emerged as a promising alternative for domain generalization. Nevertheless, the loss function is difficult to optimize for nonlinear classifiers and the original optimization objective could fail when pseudo-invariant features and geometric skews exist. Inspired by IRM, in this paper we propose a novel formulation for domain generalization, dubbed invariant information bottleneck (IIB). IIB aims at minimizing invariant risks for nonlinear classifiers and simultaneously mitigating the impact of pseudo-invariant features and geometric skews. Specifically, we first present a novel formulation for invariant causal prediction via mutual information. Then we adopt the variational formulation of the mutual information to develop a tractable loss function for nonlinear classifiers. To overcome the failure modes of IRM, we propose to minimize the mutual information between the inputs and the corresponding representations. IIB significantly outperforms IRM on synthetic datasets, where the pseudo-invariant features and geometric skews occur, showing the effectiveness of proposed formulation in overcoming failure modes of IRM. Furthermore, experiments on DomainBed show that IIB outperforms $13$ baselines by $0.9\%$ on average across $7$ real datasets.

Out-of-distribution generalization is one of the key challenges when transferring a model from the lab to the real world. Existing efforts mostly focus on building invariant features among source and target domains. Based on invariant features, a high-performing classifier on source domains could hopefully behave equally well on a target domain. In other words, the invariant features are \emph{transferable}. However, in practice, there are no perfectly transferable features, and some algorithms seem to learn ''more transferable'' features than others. How can we understand and quantify such \emph{transferability}? In this paper, we formally define transferability that one can quantify and compute in domain generalization. We point out the difference and connection with common discrepancy measures between domains, such as total variation and Wasserstein distance. We then prove that our transferability can be estimated with enough samples and give a new upper bound for the target error based on our transferability. Empirically, we evaluate the transferability of the feature embeddings learned by existing algorithms for domain generalization. Surprisingly, we find that many algorithms are not quite learning transferable features, although few could still survive. In light of this, we propose a new algorithm for learning transferable features and test it over various benchmark datasets, including RotatedMNIST, PACS, Office-Home and WILDS-FMoW. Experimental results show that the proposed algorithm achieves consistent improvement over many state-of-the-art algorithms, corroborating our theoretical findings.

Knowledge graph (KG) is a kind of efficient and informative representation of structured knowledge. A typical KG consists of a collection of knowledge triples, where each triple $(h, r, t)$ describes that the head entity $h$ and tail entity $t$ are connected through a relation $r$. Recently, extensive studies have been focusing on knowledge graph representation learning, which aims to learn low-dimensional entity and relation embeddings that are informative and scalable to use for many downstream applications, such as information retrieval~\cite{irkg}, recommendation systems~\cite{recommenderkg}, machine reading comprehension~\cite{machinereadingkg}, and query-answering systems~\cite{qakg,qakg2}. Typical KG embedding models, such as \cite{transe,conve,rotate}, usually learn the model parameters by maximizing pre-defined score functions on ground-truth triples. One major limitation of such methods is that each knowledge triple is modeled locally and independently, without considering the global contextual information of KGs. To solve this problem, another line of approaches~\cite{rgcn,compgcn} manages to model KGs as heterogeneous networks, and design message passing among entities using graph neural networks to better utilize global structural information.

With the widespread deployment of large-scale prediction systems in high-stakes domains, e.g., face recognition, criminal justice, etc., disparity on prediction accuracy between different demographic subgroups has called for fundamental understanding on the source of such disparity and algorithmic intervention to mitigate it. In this paper, we study the accuracy disparity problem in regression. To begin with, we first propose an error decomposition theorem, which decomposes the accuracy disparity into the distance between marginal label distributions and the distance between conditional representations, to help explain why such accuracy disparity appears in practice. Motivated by this error decomposition and the general idea of distribution alignment with statistical distances, we then propose an algorithm to reduce this disparity, and analyze its game-theoretic optima of the proposed objective functions. To corroborate our theoretical findings, we also conduct experiments on five benchmark datasets. The experimental results suggest that our proposed algorithms can effectively mitigate accuracy disparity while maintaining the predictive power of the regression models.

Multi-task learning (MTL) aims to improve the generalization of several related tasks by learning them jointly. As a comparison, in addition to the joint training scheme, modern meta-learning allows unseen tasks with limited labels during the test phase, in the hope of fast adaptation over them. Despite the subtle difference between MTL and meta-learning in the problem formulation, both learning paradigms share the same insight that the shared structure between existing training tasks could lead to better generalization and adaptation. In this paper, we take one important step further to understand the close connection between these two learning paradigms, through both theoretical analysis and empirical investigation. Theoretically, we first demonstrate that MTL shares the same optimization formulation with a class of gradient-based meta-learning (GBML) algorithms. We then prove that for over-parameterized neural networks with sufficient depth, the learned predictive functions of MTL and GBML are close. In particular, this result implies that the predictions given by these two models are similar over the same unseen task. Empirically, we corroborate our theoretical findings by showing that, with proper implementation, MTL is competitive against state-of-the-art GBML algorithms on a set of few-shot image classification benchmarks. Since existing GBML algorithms often involve costly second-order bi-level optimization, our first-order MTL method is an order of magnitude faster on large-scale datasets such as mini-ImageNet. We believe this work could help bridge the gap between these two learning paradigms, and provide a computationally efficient alternative to GBML that also supports fast task adaptation.

While the advent of Graph Neural Networks (GNNs) has greatly improved node and graph representation learning in many applications, the neighborhood aggregation scheme exposes additional vulnerabilities to adversaries seeking to extract node-level information about sensitive attributes. In this paper, we study the problem of protecting sensitive attributes by information obfuscation when learning with graph structured data. We propose a framework to locally filter out pre-determined sensitive attributes via adversarial training with the total variation and the Wasserstein distance. Our method creates a strong defense against inference attacks, while only suffering small loss in task performance. Theoretically, we analyze the effectiveness of our framework against a worst-case adversary, and characterize an inherent trade-off between maximizing predictive accuracy and minimizing information leakage. Experiments across multiple datasets from recommender systems, knowledge graphs and quantum chemistry demonstrate that the proposed approach provides a robust defense across various graph structures and tasks, while producing competitive GNN encoders for downstream tasks.

The success of supervised learning hinges on the assumption that the training and test data come from the same underlying distribution, which is often not valid in practice due to potential distribution shift. In light of this, most existing methods for unsupervised domain adaptation focus on achieving domain-invariant representations and small source domain error. However, recent works have shown that this is not sufficient to guarantee good generalization on the target domain, and in fact, is provably detrimental under label distribution shift. Furthermore, in many real-world applications it is often feasible to obtain a small amount of labeled data from the target domain and use them to facilitate model training with source data. Inspired by the above observations, in this paper we propose the first method that aims to simultaneously learn invariant representations and risks under the setting of semi-supervised domain adaptation (Semi-DA). First, we provide a finite sample bound for both classification and regression problems under Semi-DA. The bound suggests a principled way to obtain target generalization, i.e. by aligning both the marginal and conditional distributions across domains in feature space. Motivated by this, we then introduce the LIRR algorithm for jointly \textbf{L}earning \textbf{I}nvariant \textbf{R}epresentations and \textbf{R}isks. Finally, extensive experiments are conducted on both classification and regression tasks, which demonstrates LIRR consistently achieves state-of-the-art performance and significant improvements compared with the methods that only learn invariant representations or invariant risks.

This paper introduces Relative Predictive Coding (RPC), a new contrastive representation learning objective that maintains a good balance among training stability, minibatch size sensitivity, and downstream task performance. The key to the success of RPC is two-fold. First, RPC introduces the relative parameters to regularize the objective for boundedness and low variance. Second, RPC contains no logarithm and exponential score functions, which are the main cause of training instability in prior contrastive objectives. We empirically verify the effectiveness of RPC on benchmark vision and speech self-supervised learning tasks. Lastly, we relate RPC with mutual information (MI) estimation, showing RPC can be used to estimate MI with low variance.

Disparate impact has raised serious concerns in machine learning applications and its societal impacts. In response to the need of mitigating discrimination, fairness has been regarded as a crucial property in algorithmic design. In this work, we study the problem of disparate impact on graph-structured data. Specifically, we focus on dyadic fairness, which articulates a fairness concept that a predictive relationship between two instances should be independent of the sensitive attributes. Based on this, we theoretically relate the graph connections to dyadic fairness on link predictive scores in learning graph neural networks, and reveal that regulating weights on existing edges in a graph contributes to dyadic fairness conditionally. Subsequently, we propose our algorithm, \textbf{FairAdj}, to empirically learn a fair adjacency matrix with proper graph structural constraints for fair link prediction, and in the meanwhile preserve predictive accuracy as much as possible. Empirical validation demonstrates that our method delivers effective dyadic fairness in terms of various statistics, and at the same time enjoys a favorable fairness-utility tradeoff.

Model-based reinforcement learning methods learn a dynamics model with real data sampled from the environment and leverage it to generate simulated data to derive an agent. However, due to the potential distribution mismatch between simulated data and real data, this could lead to degraded performance. Despite much effort being devoted to reducing this distribution mismatch, existing methods fail to solve it explicitly. In this paper, we investigate how to bridge the gap between real and simulated data due to inaccurate model estimation for better policy optimization. To begin with, we first derive a lower bound of the expected return, which naturally inspires a bound maximization algorithm by aligning the simulated and real data distributions. To this end, we propose a novel model-based reinforcement learning framework AMPO, which introduces unsupervised model adaptation to minimize the integral probability metric (IPM) between feature distributions from real and simulated data. Instantiating our framework with Wasserstein-1 distance gives a practical model-based approach. Empirically, our approach achieves state-of-the-art performance in terms of sample efficiency on a range of continuous control benchmark tasks.

Since its inception, the neural estimation of mutual information (MI) has demonstrated the empirical success of modeling expected dependency between high-dimensional random variables. However, MI is an aggregate statistic and cannot be used to measure point-wise dependency between different events. In this work, instead of estimating the expected dependency, we focus on estimating point-wise dependency (PD), which quantitatively measures how likely two outcomes co-occur. We show that we can naturally obtain PD when we are optimizing MI neural variational bounds. However, optimizing these bounds is challenging due to its large variance in practice. To address this issue, we develop two methods (free of optimizing MI variational bounds): Probabilistic Classifier and Density-Ratio Fitting. We demonstrate the effectiveness of our approaches in 1) MI estimation, 2) self-supervised representation learning, and 3) cross-modal retrieval task.

Adversarial learning has demonstrated good performance in the unsupervised domain adaptation setting, by learning domain-invariant representations. However, recent work has shown limitations of this approach when label distributions differ between the source and target domains. In this paper, we propose a new assumption, \textit{generalized label shift} ($\glsa$), to improve robustness against mismatched label distributions. $\glsa$ states that, conditioned on the label, there exists a representation of the input that is invariant between the source and target domains. Under $\glsa$, we provide theoretical guarantees on the transfer performance of any classifier. We also devise necessary and sufficient conditions for $\glsa$ to hold, by using an estimation of the relative class weights between domains and an appropriate reweighting of samples. Our weight estimation method could be straightforwardly and generically applied in existing domain adaptation (DA) algorithms that learn domain-invariant representations, with small computational overhead. In particular, we modify three DA algorithms, JAN, DANN and CDAN and evaluate their performance on standard and artificial DA tasks. Our algorithms outperform the base versions, with vast improvements for large label distribution mismatches. Our code is available at \url{https://tinyurl.com/y585xt6j}.

Crowdsourced data used in machine learning services might carry sensitive information about attributes that users do not want to share. Various methods have been proposed to minimize the potential information leakage of sensitive attributes while maximizing the task accuracy. However, little is known about the theory behind these methods. In light of this gap, we develop a novel theoretical framework for attribute obfuscation. Under our framework, we propose a minimax optimization formulation to protect the given attribute and analyze its inference guarantees against worst-case adversaries. Meanwhile, there is a tension between minimizing information leakage and maximizing task accuracy. To understand this, we prove an information-theoretic lower bound to precisely characterize the fundamental trade-off between accuracy and information leakage. We conduct experiments on two real-world datasets to corroborate the inference guarantees and validate the inherent trade-offs therein. Our results indicate that, among several alternatives, the adversarial learning approach achieves the best trade-off in terms of attribute obfuscation and accuracy maximization.

Large-scale labeled training datasets have enabled deep neural networks to excel across a wide range of benchmark vision tasks. However, in many applications, it is prohibitively expensive and time-consuming to obtain large quantities of labeled data. To cope with limited labeled training data, many have attempted to directly apply models trained on a large-scale labeled source domain to another sparsely labeled or unlabeled target domain. Unfortunately, direct transfer across domains often performs poorly due to the presence of domain shift or dataset bias. Domain adaptation is a machine learning paradigm that aims to learn a model from a source domain that can perform well on a different (but related) target domain. In this paper, we review the latest single-source deep unsupervised domain adaptation methods focused on visual tasks and discuss new perspectives for future research. We begin with the definitions of different domain adaptation strategies and the descriptions of existing benchmark datasets. We then summarize and compare different categories of single-source unsupervised domain adaptation methods, including discrepancy-based methods, adversarial discriminative methods, adversarial generative methods, and self-supervision-based methods. Finally, we discuss future research directions with challenges and possible solutions.

The goal of universal machine translation is to learn to translate between any pair of languages, given a corpus of paired translated documents for a small subset of all pairs of languages. Despite impressive empirical results and an increasing interest in massively multilingual models, theoretical analysis on translation errors made by such universal machine translation models is only nascent. In this paper, we formally prove certain impossibilities of this endeavour in general, as well as prove positive results in the presence of additional (but natural) structure of data. For the former, we derive a lower bound on the translation error in the many-to-one translation setting, which shows that any algorithm aiming to learn shared sentence representations among multiple language pairs has to make a large translation error on at least one of the translation tasks, if no assumption on the structure of the languages is made. For the latter, we show that if the paired documents in the corpus follow a natural encoder-decoder generative process, we can expect a natural notion of ``generalization'': a linear number of language pairs, rather than quadratic, suffices to learn a good representation. Our theory also explains what kinds of connection graphs between pairs of languages are better suited: ones with longer paths result in worse sample complexity in terms of the total number of documents per language pair needed. We believe our theoretical insights and implications contribute to the future algorithmic design of universal machine translation.

Fair clustering aims to hide sensitive attributes during data partition by balancing the distribution of protected subgroups in each cluster. Existing work attempts to address this problem by reducing it to a classical balanced clustering with a constraint on the proportion of protected subgroups of the input space. However, the input space may limit the clustering performance, and so far only low-dimensional datasets have been considered. In light of these limitations, in this paper, we propose Deep Fair Clustering (DFC) to learn fair and clustering-favorable representations for clustering simultaneously. Our approach could effectively filter out sensitive attributes from representations, and also lead to representations that are amenable for the following cluster analysis. Theoretically, we show that our fairness constraint in DFC will not incur much loss in terms of several clustering metrics. Empirically, we provide extensive experimental demonstrations on four visual datasets to corroborate the superior performance of the proposed approach over existing fair clustering and deep clustering methods on both cluster validity and fairness criterion.

Early identification of patients at risk for postoperative complications can facilitate timely workups and treatments and improve health outcomes. Currently, a widely-used surgical risk calculator online web system developed by the American College of Surgeons (ACS) uses patients’ static features, e.g. gender, age, to assess the risk of postoperative complications. However, the most crucial signals that reflect the actual postoperative physical conditions of patients are usually real-time dynamic signals, including the vital signs of patients (e.g., heart rate, blood pressure) collected from postoperative monitoring. In this paper, we develop a dynamic postoperative complication risk scoring framework (DyCRS) to detect the “at-risk” patients in a real-time way based on postoperative sequential vital signs and static features. DyCRS is based on adaptations of the Hidden Markov Model (HMM) that captures hidden states as well as observable states to generate a real-time, probabilistic, complication risk score. Evaluating our model using electronic health record (EHR) on elective Colectomy surgery from a major health system, we show that DyCRS significantly outperforms the state-of-the-art ACS calculator and real-time predictors with 50.16% area under precision-recall curve (AUCPRC) gain on average in terms of detection effectiveness. In terms of earliness, our DyCRS can predict 15hrs55mins earlier on average than clinician's diagnosis with the recall of 60% and precision of 55%. Furthermore, Our DyCRS can extract interpretable patients' stages, which are consistent with previous medical postoperative complication studies. We believe that our contributions demonstrate significant promise for developing a more accurate, robust and interpretable postoperative complication risk scoring system, which can benefit more than 50 million annual surgeries in the US by substantially lowering adverse events and healthcare costs.

We propose a novel algorithm for learning fair representations that can simultaneously mitigate two notions of disparity among different demographic subgroups. Two key components underpinning the design of our algorithm are balanced error rate and conditional alignment of representations. We show how these two components contribute to ensuring accuracy parity and equalized false-positive and false-negative rates across groups without impacting demographic parity. Furthermore, we also demonstrate both in theory and on two real-world experiments that the proposed algorithm leads to a better utility-fairness trade-off on balanced datasets compared with existing algorithms on learning fair representations.

Approaches to continual learning aim to successfully learn a set of related tasks that arrive in an online manner. Recently, several frameworks have been developed which enable deep learning to be deployed in this learning scenario. A key modelling decision is to what extent the architecture should be shared across tasks. On the one hand, separately modelling each task avoids catastrophic forgetting but it does not support transfer learning and leads to large models. On the other hand, rigidly specifying a shared component and a task-specific part enables task transfer and limits the model size, but it is vulnerable to catastrophic forgetting and restricts the form of task-transfer that can occur. Ideally, the network should adaptively identify which parts of the network to share in a data driven way. Here we introduce such an approach called Continual Learning with Adaptive Weights (CLAW), which is based on probabilistic modelling and variational inference. Experiments show that CLAW achieves state-of-the-art performance on six benchmarks in terms of overall continual learning performance, as measured by classification accuracy, and in terms of addressing catastrophic forgetting.

With the prevalence of machine learning in high-stakes applications, especially the ones regulated by anti-discrimination laws or societal norms, it is crucial to ensure that the predictive models do not propagate any existing bias or discrimination. Due to the ability of deep neural nets to learn rich representations, recent advances in algorithmic fairness have focused on learning fair representations with adversarial techniques to reduce bias in data while preserving utility simultaneously. In this paper, through the lens of information theory, we provide the first result that quantitatively characterizes the tradeoff between demographic parity and the joint utility across different population groups. Specifically, when the base rates differ between groups, we show that any method aiming to learn fair representations admits an information-theoretic lower bound on the joint error across these groups. To complement our negative results, we also prove that if the optimal decision functions across different groups are close, then learning fair representations leads to an alternative notion of fairness, known as the accuracy parity, which states that the error rates are close between groups. Finally, our theoretical findings are also confirmed empirically on real-world datasets.

With the prevalence of machine learning services, crowdsourced data containing sensitive information poses substantial privacy challenges. Existing work focusing on protecting against membership inference attacks under the rigorous framework of differential privacy are vulnerable to attribute inference attacks. In light of the current gap between theory and practice, we develop a novel theoretical framework for privacy-preservation under the attack of attribute inference. Under our framework, we propose a minimax optimization formulation to protect the given attribute and analyze its privacy guarantees against arbitrary adversaries. On the other hand, it is clear that privacy constraint may cripple utility when the protected attribute is correlated with the target variable. To this end, we also prove an information-theoretic lower bound to precisely characterize the fundamental trade-off between utility and privacy. Empirically, we extensively conduct experiments to corroborate our privacy guarantee and validate the inherent trade-offs in different privacy preservation algorithms. Our experimental results indicate that the adversarial representation learning approaches achieve the best trade-off in terms of privacy preservation and utility maximization.

Due to the ability of deep neural nets to learn rich representations, recent advances in unsupervised domain adaptation have focused on learning domain-invariant features that achieve a small error on the source domain. The hope is that the learnt representation, together with the hypothesis learnt from the source domain, can generalize to the target domain. In this paper, we first construct a simple counterexample showing that, contrary to common belief, the above conditions are not sufficient to guarantee successful domain adaptation. In particular, the counterexample (Fig. 1) exhibits \emph{conditional shift}: the class-conditional distributions of input features change between source and target domains. To give a sufficient condition for domain adaptation, we propose a natural and interpretable generalization upper bound that explicitly takes into account the aforementioned shift. Moreover, we shed new light on the problem by proving an information-theoretic lower bound on the joint error of \emph{any} domain adaptation method that attempts to learn invariant representations. Our result characterizes a fundamental tradeoff between learning invariant representations and achieving small joint error on both domains when the marginal label distributions differ from source to target. Finally, we conduct experiments on real-world datasets that corroborate our theoretical findings. We believe these insights are helpful in guiding the future design of domain adaptation and representation learning algorithms.

Feed-forward neural networks can be understood as a combination of an intermediate representation and a linear hypothesis. While most previous works aim to diversify the representations, we explore the complementary direction by performing an adaptive and data-dependent regularization motivated by the empirical Bayes method. Specifically, we propose to construct a matrix-variate normal prior (on weights) whose covariance matrix has a Kronecker product structure. This structure is designed to capture the correlations in neurons through backpropagation. Under the assumption of this Kronecker factorization, the prior encourages neurons to borrow statistical strength from one another. Hence, it leads to an adaptive and data-dependent regularization when training networks on small datasets. To optimize the model, we present an efficient block coordinate descent algorithm with analytical solutions. Empirically, we demonstrate that the proposed method helps networks converge to local optima with smaller stable ranks and spectral norms. These properties suggest better generalizations and we present empirical results to support this expectation. We also verify the effectiveness of the approach on multiclass classification and multitask regression problems with various network structures.

We consider a multitask learning problem, in which several predictors are learned jointly. Prior research has shown that learning the relations between tasks, and between the input features, together with the predictor, can lead to better generalization and interpretability, which proved to be useful for applications in many domains. In this paper, we consider a formulation of multitask learning that learns the relationships both between tasks and between features, represented through a task covariance and a feature covariance matrix, respectively. First, we demonstrate that existing methods proposed for this problem present an issue that may lead to ill-posed optimization. We then propose an alternative formulation, as well as an efficient algorithm to optimize it. Using ideas from optimization and graph theory, we propose an efficient coordinate-wise minimization algorithm that has a closed form solution for each block subproblem. Our experiments show that the proposed optimization method is orders of magnitude faster than its competitors. We also provide a nonlinear extension that is able to achieve better generalization than existing methods.

We consider peer review under a conference setting where there are conflicts between the reviewers and the submissions. Under such conflicts, reviewers can manipulate their reviews in a strategic manner to influence the final rankings of their own papers. Present-day peer-review systems are not designed to guard against such strategic behavior, beyond minimal (and insufficient) checks such as not assigning a paper to a conflicted reviewer. In this work, we address this problem through the lens of social choice, and present a theoretical framework for strategyproof and efficient peer review. Given the conflict graph which satisfies a simple property, we first present and analyze a flexible framework for reviewer-assignment and aggregation for the reviews that guarantees not only strategyproofness but also a natural efficiency property (unanimity). Our framework is based on the so-called partitioning method, and can be treated as a generalization of this type of method to conference peer review settings. We then empirically show that the requisite property on the (authorship) conflict graph is indeed satisfied in the ICLR-17 submissions data, and further demonstrate a simple trick to make the partitioning method more practically appealing under conference peer-review settings. Finally, we complement our positive results with negative theoretical results where we prove that under slightly stronger requirements, it is impossible for any algorithm to be both strategyproof and efficient.

Strict partial order is a mathematical structure commonly seen in relational data. One obstacle to extracting such type of relations at scale is the lack of large scale labels for building effective data-driven solutions. We develop an active learning framework for mining such relations subject to a strict order. Our approach incorporates relational reasoning not only in finding new unlabeled pairs whose labels can be deduced from an existing label set, but also in devising new query strategies that consider the relational structure of labels. Our experiments on concept prerequisite relations show our proposed framework can substantially improve the classification performance with the same query budget compared to other baseline approaches.

The ability to adapt to and learn from different domains and environments is crucial for agents to generalize. In this paper we propose a probabilistic framework for domain adaptation that blends both generative and discriminative modeling in a principled way. Under this framework, generative and discriminative models correspond to specific choices of the prior over parameters. By maximizing both the marginal and the conditional log-likelihoods, our models can use both labeled instances from the source domain as well as unlabeled instances from \emph{both} source and target domains. We show that the popular reconstruction loss of autoencoder corresponds to an upper bound of the negative marginal log-likelihoods of unlabeled instances, and give a generalization bound that explicitly incorporates it into the analysis. We instantiate our framework using neural networks, and build a concrete model, DAuto.

While domain adaptation has been actively researched, most algorithms focus on the single-source-single-target adaptation setting. In this paper we propose new generalization bounds and algorithms under both classification and regression settings for unsupervised multiple source domain adaptation. Our theoretical analysis naturally leads to an efficient learning strategy using adversarial neural networks: we show how to interpret it as learning feature representations that are invariant to the multiple domain shifts while still being discriminative for the learning task. To this end, we propose multisource domain adversarial networks (MDAN) that approach domain adaptation by optimizing task-adaptive generalization bounds. To demonstrate the effectiveness of MDAN, we conduct extensive experiments showing superior adaptation performance on both classification and regression problems: sentiment analysis, digit classification, and vehicle counting.

Symmetric nonnegative matrix factorization has found abundant applications in various domains by providing a symmetric low-rank decomposition of nonnegative matrices. In this paper we propose a Frank-Wolfe (FW) solver to optimize the symmetric nonnegative matrix factorization problem under a simplicial constraint, which has recently been proposed for probabilistic clustering. Compared with existing solutions, this algorithm is simple to implement, and has no hyperparameters to be tuned. Building on the recent advances of FW algorithms in nonconvex optimization, we prove an $O(1/\eps^2)$ convergence rate to $\eps$-approximate KKT points, via a tight bound $\Theta(n^2)$ on the curvature constant, which matches the best known result in unconstrained nonconvex setting using gradient methods. Numerical results demonstrate the effectiveness of our algorithm. As a side contribution, we construct a simple nonsmooth convex problem where the FW algorithm fails to converge to the optimum. This result raises an interesting question about necessary conditions of the success of the FW algorithm on convex problems.

We propose an end-to-end model based on convolutional and recurrent neural networks for speech enhancement. Our model is purely data-driven and does not make any assumptions about the type or the stationarity of the noise. In contrast to existing methods that use multilayer perceptrons (MLPs), we employ both convolutional and recurrent neural network architectures. Thus, our approach allows us to exploit local structures in both the frequency and temporal domains. By incorporating prior knowledge of speech signals into the design of model structures, we build a model that is more data-efficient and achieves better generalization on both seen and unseen noise. Based on experiments with synthetic data, we demonstrate that our model outperforms existing methods, improving PESQ by up to 0.6 on seen noise and 0.64 on unseen noise.

We propose an approximate empirical Bayes framework and an efficient algorithm for learning the weight matrix of deep neural networks. Empirically, we show the proposed method works as a regularization approach that helps generalization when training neural networks on small datasets.

While domain adaptation has been actively researched in recent years, most theoretical results and algorithms focus on the single-source-single-target adaptation setting. Naive application of such algorithms on multiple source domain adaptation problem may lead to suboptimal solutions. We propose a new generalization bound for domain adaptation when there are multiple source domains with labeled instances and one target domain with unlabeled instances. Compared with existing bounds, the new bound does not require expert knowledge about the target distribution, nor the optimal combination rule for multisource domains. Interestingly, our theory also leads to an efficient learning strategy using adversarial neural networks: we show how to interpret it as learning feature representations that are invariant to the multiple domain shifts while still being discriminative for the learning task. To this end, we propose two models, both of which we call multisource domain adversarial networks (MDANs): the first model optimizes directly our bound, while the second model is a smoothed approximation of the first one, leading to a more data-efficient and task-adaptive model. The optimization tasks of both models are minimax saddle point problems that can be optimized by adversarial training. To demonstrate the effectiveness of MDANs, we conduct extensive experiments showing superior adaptation performance on three real-world datasets: sentiment analysis, digit classification, and vehicle counting.

Bayesian online algorithms for Sum-Product Networks (SPNs) need to update their posterior distribution after seeing one single additional instance. To do so, they must compute moments of the model parameters under this distribution. The best existing method for computing such moments scales quadratically in the size of the SPN, although it scales linearly for trees. This unfortunate scaling makes Bayesian online algorithms prohibitively expensive, except for small or tree-structured SPNs. We propose a linear-time algorithm that works even when the SPN is a general directed acyclic graph (DAG). Our algorithm significantly broadens the applicability of Bayesian online algorithms for SPNs. There are three key ingredients in the design and analysis of our algorithm: 1). For each edge in the graph, we find a linear time reduction from the moment computation problem to a joint inference problem in SPNs. 2). Using the property that each SPN computes a multilinear polynomial, we construct an efficient procedure for polynomial evaluation by differentiation without expanding the network that may contain exponentially many positive monomials. 3). We propose a dynamic programming method to further reduce the computation of the moments of all the edges in the graph from quadratic to linear. We demonstrate the usefulness of our linear time moment computation algorithm by applying it to develop a linear time assume density filter (ADF) for SPNs.

Domain adaptation addresses learning tasks where training is performed on data from one domain whereas testing is performed on data belonging to a different but related domain. Assumptions about the relationship between the source and target domains should lead to tractable solutions on the one hand, and be realistic on the other hand. Here we propose a generative domain adaptation model that allows for modeling different assumptions about this relationship, among which is a newly introduced assumption that replaces covariate shift with a possibly more realistic assumption without losing tractability due to the efficient variational inference procedure developed. In addition to the ability to model less restrictive relationships between source and target, modeling can be performed without any target labeled data (unsupervised domain adaptation). We also provide a Rademacher complexity bound of the proposed algorithm. We evaluate the model on the Amazon reviews and the CVC pedestrian detection datasets.

The assumption that data samples are independently identically distributed is the backbone of many learning algorithms. Nevertheless, datasets often exhibit rich structures in practice, and we argue that there exist some unknown orders within the data instances. Aiming to find such orders, we introduce a novel Generative Markov Network (GMN) which we use to extract the order of data instances automatically. Specifically, we assume that the instances are sampled from a Markov chain. Our goal is to learn the transitional operator of the chain as well as the generation order by maximizing the generation probability under all possible data permutations. One of our key ideas is to use neural networks as a soft lookup table for approximating the possibly huge, but discrete transition matrix. This strategy allows us to amortize the space complexity with a single model and make the transitional operator generalizable to unseen instances. To ensure the learned Markov chain is ergodic, we propose a greedy batch-wise permutation scheme that allows fast training. Empirically, we evaluate the learned Markov chain by showing that GMNs are able to discover orders among data instances and also perform comparably well to state-of-the-art methods on the one-shot recognition benchmark task.

We present a unified approach for learning the parameters of Sum-Product networks (SPNs). We prove that any complete and decomposable SPN is equivalent to a mixture of trees where each tree corresponds to a product of univariate distributions. Based on the mixture model perspective, we characterize the objective function when learning SPNs based on the maximum likelihood estimation (MLE) principle and show that the optimization problem can be formulated as a signomial program. Both the projected gradient descent (PGD) and the exponentiated gradient (EG) in this setting can be viewed as first order approximations of the signomial program after proper transformation of the objective function. Based on the signomial program formulation, we construct two parameter learning algorithms for SPNs by using sequential monomial approximations (SMA) and the concave-convex procedure (CCCP), respectively. The two proposed methods naturally admit multiplicative updates, hence effectively avoiding the projection operation. With the help of the unified framework, we also show that, in the case of SPNs, CCCP leads to the same algorithm as Expectation Maximization (EM) despite the fact that they are different in general. Extensive experiments on 20 data sets demonstrate the effectiveness and efficiency of the two proposed approaches for learning SPNs. We also show that the proposed methods can improve the performance of structure learning and yield state-of-the-art results.

Sum-Product Networks (SPNs) are probabilistic inference machines that admit exact inference in linear time in the size of the network. Existing parameter learning approaches for SPNs are largely based on the maximum likelihood principle and hence are subject to overfitting compared to more Bayesian approaches. Exact Bayesian posterior inference for SPNs is computationally intractable. Both standard variational inference and posterior sampling for SPNs are computationally infeasible even for networks of moderate size due to the large number of local latent variables per instance. In this work, we propose a novel deterministic collapsed variational inference algorithm for SPNs that is computationally efficient, easy to implement and at the same time allows us to incorporate prior information into the optimization formulation. Extensive experiments show a significant improvement in accuracy compared with a maximum likelihood based approach.

Sum-product networks (SPNs) have recently emerged as an attractive representation due to their dual interpretation as a special type of deep neural network with clear semantics and a tractable probabilistic graphical model. We explore online algorithms for parameter learning in SPNs with continuous variables. More specifically, we consider SPNs with Gaussian leaf distributions and show how to derive an online Bayesian moment matching algorithm to learn from streaming data. We compare the resulting generative models to stacked restricted Boltzmann machines and generative moment matching networks on real-world datasets.

Probabilistic graphical models provide a general and flexible framework for reasoning about complex dependencies in noisy domains with many variables. Among the various types of probabilistic graphical models, sum-product networks (SPNs) have recently generated some interest because exact inference can always be done in linear time with respect to the size of the network. This is particularly attractive since it means that learning an SPN from data always yields a tractable model for inference. However, existing parameter learning algorithms for SPNs operate in batch mode and do not scale easily to large datasets. In this work, we explore online algorithms to ensure that parameter learning can also be done tractably with respect to the amount of data. More specifically, we propose a new Bayesian moment matching (BMM) algorithm that operates naturally in an online fashion and that can be easily distributed. We demonstrate the effectiveness and scalability of BMM in comparison to online extensions of gradient descent and expectation maximization on 20 classic benchmarks and 4 large scale datasets.

In this paper, we establish some theoretical connections between Sum-Product Networks (SPNs) and Bayesian Networks (BNs). We prove that every SPN can be converted into a BN in linear time and space in terms of the network size. The key insight is to use Algebraic Decision Diagrams (ADDs) to compactly represent the local conditional probability distributions at each node in the resulting BN by exploiting context-specific independence (CSI). The generated BN has a simple directed bipartite graphical structure. We show that by applying the Variable Elimination algorithm (VE) to the generated BN with ADD representations, we can recover the original SPN where the SPN can be viewed as a history record or caching of the VE inference process. To help state the proof clearly, we introduce the notion of {\em normal} SPN and present a theoretical analysis of the consistency and decomposability properties. We conclude the paper with some discussion of the implications of the proof and establish a connection between the depth of an SPN and a lower bound of the tree-width of its corresponding BN.

The ability to accurately model a sentence at varying stages (e.g., word-phrase-sentence) plays a central role in natural language processing. As an effort towards this goal we propose a self-adaptive hierarchical sentence model (AdaSent). AdaSent effectively forms a hierarchy of representations from words to phrases and then to sentences through recursive gated local composition of adjacent segments. We design a competitive mechanism (through gating networks) to allow the representations of the same sentence to be engaged in a particular learning task (e.g., classification), therefore effectively mitigating the gradient vanishing problem persistent in other recursive models. Both qualitative and quantitative analysis shows that AdaSent can automatically form and select the representations suitable for the task at hand during training, yielding superior classification performance over competitor models on 5 benchmark data sets.

We propose SoF (Soft-cluster matrix Factorization), a probabilistic clustering algorithm which softly assigns each data point into clusters. Unlike model-based clustering algorithms, SoF does not make assumptions about the data density distribution. Instead, we take an axiomatic approach to define 4 properties that the probability of co-clustered pairs of points should satisfy. Based on the properties, SoF utilizes a distance measure between pairs of points to induce the conditional co-cluster probabilities. The objective function in our framework establishes an important connection between probabilistic clustering and constrained symmetric Nonnegative Matrix Factorization (NMF), hence providing a theoretical interpretation for NMF-based clustering algorithms. To optimize the objective, we derive a sequential minimization algorithm using a penalty method. Experimental results on both synthetic and real-world datasets show that SoF significantly outperforms previous NMF-based algorithms and that it is able to detect non-convex patterns as well as cluster boundaries.

Analogous to sequence alignment, network alignment (NA) can be used to transfer biological knowledge across species between conserved network regions. NA faces two algorithmic challenges: 1) Which cost function to use to capture “similarities” between nodes in different networks? 2) Which alignment strategy to use to rapidly identify “high-scoring” alignments from all possible alignments? We “break down” existing state-of-the-art methods that use both different cost functions and different alignment strategies to evaluate each combination of their cost functions and alignment strategies. We find that a combination of the cost function of one method and the alignment strategy of another method beats the existing methods. Hence, we propose this combination as a novel superior NA method. Then, since human aging is hard to study experimentally due to long lifespan, we use NA to transfer aging-related knowledge from well annotated model species to poorly annotated human. By doing so, we produce novel human aging-related knowledge, which complements currently available knowledge about aging that has been obtained mainly by sequence alignment. We demonstrate significant similarity between topological and functional properties of our novel predictions and those of known aging-related genes. We are the first to use NA to learn more about aging.

Spectral learning recently generated lots of excitement in machine learning, largely because it is the first known method to produce consistent estimates (under suitable conditions) for several latent variable models. In contrast, maximum likelihood estimates may get trapped in local optima due to the non-convex nature of the likelihood function of latent variable models. In this paper, we do an empirical evaluation of spectral learning (SL) and expectation maximization (EM), which reveals an important gap between the theory and the practice. First, SL often leads to negative probabilities. Second, EM often yields better estimates than spectral learning and it does not seem to get stuck in local optima. We discuss how the rank of the model parameters and the amount of training data can yield negative probabilities. We also question the common belief that maximum likelihood estimators are necessarily inconsistent.