Han Zhao

Yifei He, Haoxiang Wang, Bo Li et al.

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 $\textbf{G}$enerative Gradual D$\textbf{O}$main $\textbf{A}$daptation with Optimal $\textbf{T}$ransport (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/uiuctml/GOAT.

Zikun Chen, Han Zhao, Parham Aarabi et al.

Generative Adversarial Networks (GANs) can synthesize realistic images, with the learned latent space shown to encode rich semantic information with various interpretable directions. However, due to the unstructured nature of the learned latent space, it inherits the bias from the training data where specific groups of visual attributes that are not causally related tend to appear together, a phenomenon also known as spurious correlations, e.g., age and eyeglasses or women and lipsticks. Consequently, the learned distribution often lacks the proper modelling of the missing examples. The interpolation following editing directions for one attribute could result in entangled changes with other attributes. To address this problem, previous works typically adjust the learned directions to minimize the changes in other attributes, yet they still fail on strongly correlated features. In this work, we study the entanglement issue in both the training data and the learned latent space for the StyleGAN2-FFHQ model. We propose a novel framework SC$^2$GAN that achieves disentanglement by re-projecting low-density latent code samples in the original latent space and correcting the editing directions based on both the high-density and low-density regions. By leveraging the original meaningful directions and semantic region-specific layers, our framework interpolates the original latent codes to generate images with attribute combination that appears infrequently, then inverts these samples back to the original latent space. We apply our framework to pre-existing methods that learn meaningful latent directions and showcase its strong capability to disentangle the attributes with small amounts of low-density region samples added.

Makoto Yamada, Yuki Takezawa, Guillaume Houry et al.

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.

Remi Tachet, Han Zhao, Yu-Xiang Wang et al.

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, generalized label shift ($GLS$), to improve robustness against mismatched label distributions. $GLS$ states that, conditioned on the label, there exists a representation of the input that is invariant between the source and target domains. Under $GLS$, we provide theoretical guarantees on the transfer performance of any classifier. We also devise necessary and sufficient conditions for $GLS$ 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 https://tinyurl.com/y585xt6j.

Han Zhao, Wenxuan Song, Donglin Wang et al.

Developing versatile quadruped robots that can smoothly perform various actions and tasks in real-world environments remains a significant challenge. This paper introduces a novel vision-language-action (VLA) model, mixture of robotic experts (MoRE), for quadruped robots that aim to introduce reinforcement learning (RL) for fine-tuning large-scale VLA models with a large amount of mixed-quality data. MoRE integrates multiple low-rank adaptation modules as distinct experts within a dense multi-modal large language model (MLLM), forming a sparse-activated mixture-of-experts model. This design enables the model to effectively adapt to a wide array of downstream tasks. Moreover, we employ a reinforcement learning-based training objective to train our model as a Q-function after deeply exploring the structural properties of our tasks. Effective learning from automatically collected mixed-quality data enhances data efficiency and model performance. Extensive experiments demonstrate that MoRE outperforms all baselines across six different skills and exhibits superior generalization capabilities in out-of-distribution scenarios. We further validate our method in real-world scenarios, confirming the practicality of our approach and laying a solid foundation for future research on multi-task learning in quadruped robots.

Xun Jiang, Feng Li, Han Zhao et al.

Large language models (LLMs) like GPTs, trained on vast datasets, have demonstrated impressive capabilities in language understanding, reasoning, and planning, achieving human-level performance in various tasks. Most studies focus on enhancing these models by training on ever-larger datasets to build more powerful foundation models. While training stronger models is important, enabling models to evolve during inference is equally crucial, a process we refer to as AI self-evolution. Unlike large-scale training, self-evolution may rely on limited data or interactions. Inspired by the columnar organization of the human cerebral cortex, we hypothesize that AI models could develop cognitive abilities and build internal representations through iterative interactions with their environment. To achieve this, models need long-term memory (LTM) to store and manage processed interaction data. LTM supports self-evolution by representing diverse experiences across environments and agents. In this report, we explore AI self-evolution and its potential to enhance models during inference. We examine LTM's role in lifelong learning, allowing models to evolve based on accumulated interactions. We outline the structure of LTM and the systems needed for effective data retention and representation. We also classify approaches for building personalized models with LTM data and show how these models achieve self-evolution through interaction. Using LTM, our multi-agent framework OMNE achieved first place on the GAIA benchmark, demonstrating LTM's potential for AI self-evolution. Finally, we present a roadmap for future research, emphasizing the importance of LTM for advancing AI technology and its practical applications.

Xudong Liu, Zikun Chen, Ruowei Jiang et al.

Recent advances in diffusion models have enabled high-quality generation and manipulation of images guided by texts, as well as concept learning from images. However, naive applications of existing methods to editing tasks that require fine-grained control, e.g., face editing, often lead to suboptimal solutions with identity information and high-frequency details lost during the editing process, or irrelevant image regions altered due to entangled concepts. In this work, we propose S$^2$Edit, a novel method based on a pre-trained text-to-image diffusion model that enables personalized editing with precise semantic and spatial control. We first fine-tune our model to embed the identity information into a learnable text token. During fine-tuning, we disentangle the learned identity token from attributes to be edited by enforcing an orthogonality constraint in the textual feature space. To ensure that the identity token only affects regions of interest, we apply object masks to guide the cross-attention maps. At inference time, our method performs localized editing while faithfully preserving the original identity with semantically disentangled and spatially focused identity token learned. Extensive experiments demonstrate the superiority of S$^2$Edit over state-of-the-art methods both quantitatively and qualitatively. Additionally, we showcase several compositional image editing applications of S$^2$Edit such as makeup transfer.

Jianfeng Chi, Jian Shen, Xinyi Dai et al.

Algorithmic decisions made by machine learning models in high-stakes domains may have lasting impacts over time. However, 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 sharing the same state and action spaces 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.

Haoxiang Wang, Han Zhao, Bo Li

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.

Shiji Zhou, Han Zhao, Shanghang Zhang et al.

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 $O({T}^{2/3})$ dynamic regret bound under mild assumptions, which is aligned with the $Ω(T^{2/3})$ lower bound of online learning algorithms with full labels. In the general case, we show a regret bound of $O({T}^{2/3} + α^* T)$, where $α^*$ 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.

Guojun Zhang, Han Zhao, Yaoliang Yu et al.

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.

Jianfeng Chi, Yuan Tian, Geoffrey J. Gordon et al.

With the widespread deployment of large-scale prediction systems in high-stakes domains, e.g., face recognition, criminal justice, etc., disparity in 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.

Han Zhao, Chen Dan, Bryon Aragam et al.

A wide range of machine learning applications such as privacy-preserving learning, algorithmic fairness, and domain adaptation/generalization among others, involve learning 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.

Jian Shen, Han Zhao, Weinan Zhang et al.

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.

Bo Li, Yezhen Wang, Shanghang Zhang et al.

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.

Peiyuan Liao, Han Zhao, Keyulu Xu et al.

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.

Huajie Shao, Haohong Lin, Qinmin Yang et al.

This paper challenges the common assumption that the weight $β$, in $β$-VAE, should be larger than $1$ in order to effectively disentangle latent factors. We demonstrate that $β$-VAE, with $β< 1$, can not only attain good disentanglement but also significantly improve reconstruction accuracy via dynamic control. The paper removes the inherent trade-off between reconstruction accuracy and disentanglement for $β$-VAE. Existing methods, such as $β$-VAE and FactorVAE, assign a large weight to the KL-divergence term in the objective function, leading to high reconstruction errors for the sake of better disentanglement. To mitigate this problem, a ControlVAE has recently been developed that dynamically tunes the KL-divergence weight in an attempt to control the trade-off to more a favorable point. However, ControlVAE fails to eliminate the conflict between the need for a large $β$ (for disentanglement) and the need for a small $β$. Instead, we propose DynamicVAE that maintains a different $β$ at different stages of training, thereby decoupling disentanglement and reconstruction accuracy. In order to evolve the weight, $β$, along a trajectory that enables such decoupling, DynamicVAE leverages a modified incremental PI (proportional-integral) controller, 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. We theoretically prove the stability of the proposed approach. Evaluation results on three benchmark datasets demonstrate that DynamicVAE significantly improves the reconstruction accuracy while achieving disentanglement comparable to the best of existing methods. The results verify that our method can separate disentangled representation learning and reconstruction, removing the inherent tension between the two.

Sicheng Zhao, Xiangyu Yue, Shanghang Zhang et al.

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.

Han Zhao, Junjie Hu, Andrej Risteski

The goal of universal machine translation is to learn to translate between any pair of languages, given a corpus of paired translated documents for \emph{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-many 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 \emph{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.

Yao-Hung Hubert Tsai, Han Zhao, Makoto Yamada et al.

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.

Tameem Adel, Han Zhao, Richard E. Turner

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.

Han Zhao, Amanda Coston, Tameem Adel et al.

We propose a novel algorithm for learning fair representations that can simultaneously mitigate two notions of disparity among different demographic subgroups in the classification setting. 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 for classification.

Han Zhao, Yao-Hung Hubert Tsai, Ruslan Salakhutdinov et al.

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.

Han Zhao, Geoffrey J. Gordon

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 that 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.

Han Zhao, Jianfeng Chi, Yuan Tian et al.

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, it is clear that in general 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 this trade-off. Our results indicate that, among several alternatives, the adversarial learning approach achieves the best trade-off in terms of attribute obfuscation and accuracy maximization.

Han Zhao, Remi Tachet des Combes, Kun Zhang et al.

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 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.

Yichong Xu, Han Zhao, Xiaofei Shi et al.

We consider peer review in a conference setting where there is typically an overlap between the set of reviewers and the set of authors. This overlap can incentivize strategic reviews to influence the final ranking of one's own papers. In this work, we address this problem through the lens of social choice, and present a theoretical framework for strategyproof and efficient peer review. We first present and analyze an algorithm for reviewer-assignment and aggregation that guarantees strategyproofness and a natural efficiency property called unanimity, when the authorship graph satisfies a simple property. Our algorithm is based on the so-called partitioning method, and can be thought as a generalization of this method to conference peer review settings. We then empirically show that the requisite property on the authorship graph is indeed satisfied in the submission data from the ICLR conference, and further demonstrate a simple trick to make the partitioning method more practically appealing for conference peer review. Finally, we complement our positive results with negative theoretical results where we prove that under various ways of strengthening the requirements, it is impossible for any algorithm to be strategyproof and efficient.

Chen Liang, Jianbo Ye, Han Zhao et al.

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.

Han Zhao, Geoff Gordon

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 $O(1/\varepsilon^2)$ convergence rate to $\varepsilon$-approximate KKT points, via a tight bound $Θ(n^2)$ 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.

Han Zhao, Shanghang Zhang, Guanhang Wu et al.

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. As a step toward bridging the gap, 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.

Han Zhao, Zhenyao Zhu, Junjie Hu et al.

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. This provides us a very general way to interpolate between generative and discriminative extremes through different choices of priors. By maximizing both the marginal and the conditional log-likelihoods, models derived from this framework can use both labeled instances from the source domain as well as unlabeled instances from both source and target domains. Under this framework, we show that the popular reconstruction loss of autoencoder corresponds to an upper bound of the negative marginal log-likelihoods of unlabeled instances, where marginal distributions are given by proper kernel density estimations. This provides a way to interpret the empirical success of autoencoders in domain adaptation and semi-supervised learning. We instantiate our framework using neural networks, and build a concrete model, DAuto. Empirically, we demonstrate the effectiveness of DAuto on text, image and speech datasets, showing that it outperforms related competitors when domain adaptation is possible.

Han Zhao, Geoff Gordon

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 an optimal linear-time algorithm that works even when the SPN is a general directed acyclic graph (DAG), which 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 construct 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 give an efficient procedure for polynomial evaluation by differentiation without expanding the network that may contain exponentially many 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 algorithm by applying it to develop a linear time assume density filter (ADF) for SPNs.

Han Zhao, Otilia Stretcu, Alex Smola et al.

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.

Han Zhao, Pascal Poupart, Geoff Gordon

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. 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.

Han Zhao, Pascal Poupart

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.