arXiv subjects

Linjun Zhang

Publications and source records attributed to Linjun Zhang.

At least 91 records · Page 5Linked to original sources

arXiv2023

Discover and Cure: Concept-aware Mitigation of Spurious Correlation

Deep neural networks often rely on spurious correlations to make predictions, which hinders generalization beyond training environments. For instance, models that associate cats with bed backgrounds can fail to predict the existence of cats in other environments without beds. Mitigating spurious correlations is crucial in building trustworthy models. However, the existing works lack transparency to offer insights into the mitigation process. In this work, we propose an interpretable framework, Discover and Cure (DISC), to tackle the issue. With human-interpretable concepts, DISC iteratively 1) discovers unstable concepts across different environments as spurious attributes, then 2) intervenes on the training data using the discovered concepts to reduce spurious correlation. Across systematic experiments, DISC provides superior generalization ability and interpretability than the existing approaches. Specifically, it outperforms the state-of-the-art methods on an object recognition task and a skin-lesion classification task by 7.5% and 9.6%, respectively. Additionally, we offer theoretical analysis and guarantees to understand the benefits of models trained by DISC. Code and data are available at https://github.com/Wuyxin/DISC.

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arXiv2023

Understanding Multimodal Contrastive Learning and Incorporating Unpaired Data

Language-supervised vision models have recently attracted great attention in computer vision. A common approach to build such models is to use contrastive learning on paired data across the two modalities, as exemplified by Contrastive Language-Image Pre-Training (CLIP). In this paper, under linear representation settings, (i) we initiate the investigation of a general class of nonlinear loss functions for multimodal contrastive learning (MMCL) including CLIP loss and show its connection to singular value decomposition (SVD). Namely, we show that each step of loss minimization by gradient descent can be seen as performing SVD on a contrastive cross-covariance matrix. Based on this insight, (ii) we analyze the performance of MMCL. We quantitatively show that the feature learning ability of MMCL can be better than that of unimodal contrastive learning applied to each modality even under the presence of wrongly matched pairs. This characterizes the robustness of MMCL to noisy data. Furthermore, when we have access to additional unpaired data, (iii) we propose a new MMCL loss that incorporates additional unpaired datasets. We show that the algorithm can detect the ground-truth pairs and improve performance by fully exploiting unpaired datasets. The performance of the proposed algorithm was verified by numerical experiments.

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arXiv2023

HappyMap: A Generalized Multi-calibration Method

Multi-calibration is a powerful and evolving concept originating in the field of algorithmic fairness. For a predictor $f$ that estimates the outcome $y$ given covariates $x$, and for a function class $\mathcal{C}$, multi-calibration requires that the predictor $f(x)$ and outcome $y$ are indistinguishable under the class of auditors in $\mathcal{C}$. Fairness is captured by incorporating demographic subgroups into the class of functions~$\mathcal{C}$. Recent work has shown that, by enriching the class $\mathcal{C}$ to incorporate appropriate propensity re-weighting functions, multi-calibration also yields target-independent learning, wherein a model trained on a source domain performs well on unseen, future, target domains(approximately) captured by the re-weightings. Formally, multi-calibration with respect to $\mathcal{C}$ bounds $\big|\mathbb{E}_{(x,y)\sim \mathcal{D}}[c(f(x),x)\cdot(f(x)-y)]\big|$ for all $c \in \mathcal{C}$. In this work, we view the term $(f(x)-y)$ as just one specific mapping, and explore the power of an enriched class of mappings. We propose \textit{HappyMap}, a generalization of multi-calibration, which yields a wide range of new applications, including a new fairness notion for uncertainty quantification (conformal prediction), a novel technique for conformal prediction under covariate shift, and a different approach to analyzing missing data, while also yielding a unified understanding of several existing seemingly disparate algorithmic fairness notions and target-independent learning approaches. We give a single \textit{HappyMap} meta-algorithm that captures all these results, together with a sufficiency condition for its success.

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arXiv2022

Reinforcement Learning with Stepwise Fairness Constraints

AI methods are used in societally important settings, ranging from credit to employment to housing, and it is crucial to provide fairness in regard to algorithmic decision making. Moreover, many settings are dynamic, with populations responding to sequential decision policies. We introduce the study of reinforcement learning (RL) with stepwise fairness constraints, requiring group fairness at each time step. Our focus is on tabular episodic RL, and we provide learning algorithms with strong theoretical guarantees in regard to policy optimality and fairness violation. Our framework provides useful tools to study the impact of fairness constraints in sequential settings and brings up new challenges in RL.

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arXiv2022

C-Mixup: Improving Generalization in Regression

Improving the generalization of deep networks is an important open challenge, particularly in domains without plentiful data. The mixup algorithm improves generalization by linearly interpolating a pair of examples and their corresponding labels. These interpolated examples augment the original training set. Mixup has shown promising results in various classification tasks, but systematic analysis of mixup in regression remains underexplored. Using mixup directly on regression labels can result in arbitrarily incorrect labels. In this paper, we propose a simple yet powerful algorithm, C-Mixup, to improve generalization on regression tasks. In contrast with vanilla mixup, which picks training examples for mixing with uniform probability, C-Mixup adjusts the sampling probability based on the similarity of the labels. Our theoretical analysis confirms that C-Mixup with label similarity obtains a smaller mean square error in supervised regression and meta-regression than vanilla mixup and using feature similarity. Another benefit of C-Mixup is that it can improve out-of-distribution robustness, where the test distribution is different from the training distribution. By selectively interpolating examples with similar labels, it mitigates the effects of domain-associated information and yields domain-invariant representations. We evaluate C-Mixup on eleven datasets, ranging from tabular to video data. Compared to the best prior approach, C-Mixup achieves 6.56%, 4.76%, 5.82% improvements in in-distribution generalization, task generalization, and out-of-distribution robustness, respectively. Code is released at https://github.com/huaxiuyao/C-Mixup.

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arXiv2022

When and How Mixup Improves Calibration

In many machine learning applications, it is important for the model to provide confidence scores that accurately capture its prediction uncertainty. Although modern learning methods have achieved great success in predictive accuracy, generating calibrated confidence scores remains a major challenge. Mixup, a popular yet simple data augmentation technique based on taking convex combinations of pairs of training examples, has been empirically found to significantly improve confidence calibration across diverse applications. However, when and how Mixup helps calibration is still a mystery. In this paper, we theoretically prove that Mixup improves calibration in \textit{high-dimensional} settings by investigating natural statistical models. Interestingly, the calibration benefit of Mixup increases as the model capacity increases. We support our theories with experiments on common architectures and datasets. In addition, we study how Mixup improves calibration in semi-supervised learning. While incorporating unlabeled data can sometimes make the model less calibrated, adding Mixup training mitigates this issue and provably improves calibration. Our analysis provides new insights and a framework to understand Mixup and calibration.

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arXiv2022

Improving Out-of-Distribution Robustness via Selective Augmentation

Machine learning algorithms typically assume that training and test examples are drawn from the same distribution. However, distribution shift is a common problem in real-world applications and can cause models to perform dramatically worse at test time. In this paper, we specifically consider the problems of subpopulation shifts (e.g., imbalanced data) and domain shifts. While prior works often seek to explicitly regularize internal representations or predictors of the model to be domain invariant, we instead aim to learn invariant predictors without restricting the model's internal representations or predictors. This leads to a simple mixup-based technique which learns invariant predictors via selective augmentation called LISA. LISA selectively interpolates samples either with the same labels but different domains or with the same domain but different labels. Empirically, we study the effectiveness of LISA on nine benchmarks ranging from subpopulation shifts to domain shifts, and we find that LISA consistently outperforms other state-of-the-art methods and leads to more invariant predictors. We further analyze a linear setting and theoretically show how LISA leads to a smaller worst-group error.

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arXiv2022

FIFA: Making Fairness More Generalizable in Classifiers Trained on Imbalanced Data

Algorithmic fairness plays an important role in machine learning and imposing fairness constraints during learning is a common approach. However, many datasets are imbalanced in certain label classes (e.g. "healthy") and sensitive subgroups (e.g. "older patients"). Empirically, this imbalance leads to a lack of generalizability not only of classification, but also of fairness properties, especially in over-parameterized models. For example, fairness-aware training may ensure equalized odds (EO) on the training data, but EO is far from being satisfied on new users. In this paper, we propose a theoretically-principled, yet Flexible approach that is Imbalance-Fairness-Aware (FIFA). Specifically, FIFA encourages both classification and fairness generalization and can be flexibly combined with many existing fair learning methods with logits-based losses. While our main focus is on EO, FIFA can be directly applied to achieve equalized opportunity (EqOpt); and under certain conditions, it can also be applied to other fairness notions. We demonstrate the power of FIFA by combining it with a popular fair classification algorithm, and the resulting algorithm achieves significantly better fairness generalization on several real-world datasets.

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arXiv2022

Understanding Dynamics of Nonlinear Representation Learning and Its Application

Representations of the world environment play a crucial role in artificial intelligence. It is often inefficient to conduct reasoning and inference directly in the space of raw sensory representations, such as pixel values of images. Representation learning allows us to automatically discover suitable representations from raw sensory data. For example, given raw sensory data, a deep neural network learns nonlinear representations at its hidden layers, which are subsequently used for classification (or regression) at its output layer. This happens implicitly during training through minimizing a supervised or unsupervised loss in common practical regimes of deep learning, unlike the neural tangent kernel (NTK) regime. In this paper, we study the dynamics of such implicit nonlinear representation learning, which is beyond the NTK regime. We identify a pair of a new assumption and a novel condition, called the common model structure assumption and the data-architecture alignment condition. Under the common model structure assumption, the data-architecture alignment condition is shown to be sufficient for the global convergence and necessary for the global optimality. Moreover, our theory explains how and when increasing the network size does and does not improve the training behaviors in the practical regime. Our results provide practical guidance for designing a model structure: e.g., the common model structure assumption can be used as a justification for using a particular model structure instead of others. We also derive a new training framework based on the theory. The proposed framework is empirically shown to maintain competitive (practical) test performances while providing global convergence guarantees for deep residual neural networks with convolutions, skip connections, and batch normalization with standard benchmark datasets, including CIFAR-10, CIFAR-100, and SVHN.

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arXiv2022

Meta-Learning with Fewer Tasks through Task Interpolation

Meta-learning enables algorithms to quickly learn a newly encountered task with just a few labeled examples by transferring previously learned knowledge. However, the bottleneck of current meta-learning algorithms is the requirement of a large number of meta-training tasks, which may not be accessible in real-world scenarios. To address the challenge that available tasks may not densely sample the space of tasks, we propose to augment the task set through interpolation. By meta-learning with task interpolation (MLTI), our approach effectively generates additional tasks by randomly sampling a pair of tasks and interpolating the corresponding features and labels. Under both gradient-based and metric-based meta-learning settings, our theoretical analysis shows MLTI corresponds to a data-adaptive meta-regularization and further improves the generalization. Empirically, in our experiments on eight datasets from diverse domains including image recognition, pose prediction, molecule property prediction, and medical image classification, we find that the proposed general MLTI framework is compatible with representative meta-learning algorithms and consistently outperforms other state-of-the-art strategies.

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arXiv2021

Scaffolding Sets

Predictors map individual instances in a population to the interval $[0,1]$. For a collection $\mathcal C$ of subsets of a population, a predictor is multi-calibrated with respect to $\mathcal C$ if it is simultaneously calibrated on each set in $\mathcal C$. We initiate the study of the construction of scaffolding sets, a small collection $\mathcal S$ of sets with the property that multi-calibration with respect to $\mathcal S$ ensures correctness, and not just calibration, of the predictor. Our approach is inspired by the folk wisdom that the intermediate layers of a neural net learn a highly structured and useful data representation.

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arXiv2021

High-Dimensional Differentially-Private EM Algorithm: Methods and Near-Optimal Statistical Guarantees

In this paper, we develop a general framework to design differentially private expectation-maximization (EM) algorithms in high-dimensional latent variable models, based on the noisy iterative hard-thresholding. We derive the statistical guarantees of the proposed framework and apply it to three specific models: Gaussian mixture, mixture of regression, and regression with missing covariates. In each model, we establish the near-optimal rate of convergence with differential privacy constraints, and show the proposed algorithm is minimax rate optimal up to logarithm factors. The technical tools developed for the high-dimensional setting are then extended to the classic low-dimensional latent variable models, and we propose a near rate-optimal EM algorithm with differential privacy guarantees in this setting. Simulation studies and real data analysis are conducted to support our results.

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arXiv2021

Adversarial Training Helps Transfer Learning via Better Representations

Transfer learning aims to leverage models pre-trained on source data to efficiently adapt to target setting, where only limited data are available for model fine-tuning. Recent works empirically demonstrate that adversarial training in the source data can improve the ability of models to transfer to new domains. However, why this happens is not known. In this paper, we provide a theoretical model to rigorously analyze how adversarial training helps transfer learning. We show that adversarial training in the source data generates provably better representations, so fine-tuning on top of this representation leads to a more accurate predictor of the target data. We further demonstrate both theoretically and empirically that semi-supervised learning in the source data can also improve transfer learning by similarly improving the representation. Moreover, performing adversarial training on top of semi-supervised learning can further improve transferability, suggesting that the two approaches have complementary benefits on representations. We support our theories with experiments on popular data sets and deep learning architectures.

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arXiv2021

Improving Generalization in Meta-learning via Task Augmentation

Meta-learning has proven to be a powerful paradigm for transferring the knowledge from previous tasks to facilitate the learning of a novel task. Current dominant algorithms train a well-generalized model initialization which is adapted to each task via the support set. The crux lies in optimizing the generalization capability of the initialization, which is measured by the performance of the adapted model on the query set of each task. Unfortunately, this generalization measure, evidenced by empirical results, pushes the initialization to overfit the meta-training tasks, which significantly impairs the generalization and adaptation to novel tasks. To address this issue, we actively augment a meta-training task with "more data" when evaluating the generalization. Concretely, we propose two task augmentation methods, including MetaMix and Channel Shuffle. MetaMix linearly combines features and labels of samples from both the support and query sets. For each class of samples, Channel Shuffle randomly replaces a subset of their channels with the corresponding ones from a different class. Theoretical studies show how task augmentation improves the generalization of meta-learning. Moreover, both MetaMix and Channel Shuffle outperform state-of-the-art results by a large margin across many datasets and are compatible with existing meta-learning algorithms.

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arXiv2021

How Does Mixup Help With Robustness and Generalization?

Mixup is a popular data augmentation technique based on taking convex combinations of pairs of examples and their labels. This simple technique has been shown to substantially improve both the robustness and the generalization of the trained model. However, it is not well-understood why such improvement occurs. In this paper, we provide theoretical analysis to demonstrate how using Mixup in training helps model robustness and generalization. For robustness, we show that minimizing the Mixup loss corresponds to approximately minimizing an upper bound of the adversarial loss. This explains why models obtained by Mixup training exhibits robustness to several kinds of adversarial attacks such as Fast Gradient Sign Method (FGSM). For generalization, we prove that Mixup augmentation corresponds to a specific type of data-adaptive regularization which reduces overfitting. Our analysis provides new insights and a framework to understand Mixup.

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arXiv2021

A Central Limit Theorem for Differentially Private Query Answering

Perhaps the single most important use case for differential privacy is to privately answer numerical queries, which is usually achieved by adding noise to the answer vector. The central question, therefore, is to understand which noise distribution optimizes the privacy-accuracy trade-off, especially when the dimension of the answer vector is high. Accordingly, extensive literature has been dedicated to the question and the upper and lower bounds have been matched up to constant factors [BUV18, SU17]. In this paper, we take a novel approach to address this important optimality question. We first demonstrate an intriguing central limit theorem phenomenon in the high-dimensional regime. More precisely, we prove that a mechanism is approximately Gaussian Differentially Private [DRS21] if the added noise satisfies certain conditions. In particular, densities proportional to $\mathrm{e}^{-\|x\|_p^α}$, where $\|x\|_p$ is the standard $\ell_p$-norm, satisfies the conditions. Taking this perspective, we make use of the Cramer--Rao inequality and show an "uncertainty principle"-style result: the product of the privacy parameter and the $\ell_2$-loss of the mechanism is lower bounded by the dimension. Furthermore, the Gaussian mechanism achieves the constant-sharp optimal privacy-accuracy trade-off among all such noises. Our findings are corroborated by numerical experiments.

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arXiv2021

Improving Adversarial Robustness via Unlabeled Out-of-Domain Data

Data augmentation by incorporating cheap unlabeled data from multiple domains is a powerful way to improve prediction especially when there is limited labeled data. In this work, we investigate how adversarial robustness can be enhanced by leveraging out-of-domain unlabeled data. We demonstrate that for broad classes of distributions and classifiers, there exists a sample complexity gap between standard and robust classification. We quantify to what degree this gap can be bridged via leveraging unlabeled samples from a shifted domain by providing both upper and lower bounds. Moreover, we show settings where we achieve better adversarial robustness when the unlabeled data come from a shifted domain rather than the same domain as the labeled data. We also investigate how to leverage out-of-domain data when some structural information, such as sparsity, is shared between labeled and unlabeled domains. Experimentally, we augment two object recognition datasets (CIFAR-10 and SVHN) with easy to obtain and unlabeled out-of-domain data and demonstrate substantial improvement in the model's robustness against $\ell_\infty$ adversarial attacks on the original domain.

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arXiv2020

The Cost of Privacy in Generalized Linear Models: Algorithms and Minimax Lower Bounds

We propose differentially private algorithms for parameter estimation in both low-dimensional and high-dimensional sparse generalized linear models (GLMs) by constructing private versions of projected gradient descent. We show that the proposed algorithms are nearly rate-optimal by characterizing their statistical performance and establishing privacy-constrained minimax lower bounds for GLMs. The lower bounds are obtained via a novel technique, which is based on Stein's Lemma and generalizes the tracing attack technique for privacy-constrained lower bounds. This lower bound argument can be of independent interest as it is applicable to general parametric models. Simulated and real data experiments are conducted to demonstrate the numerical performance of our algorithms.

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