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Researcher profile

Shihua Zhang

Shihua Zhang contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningComputer VisionArtificial IntelligenceDistributed, Parallel, and Cluster Computingmath.OCMethodology

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Published work

8 published item(s)

preprint2026arXiv

Deciphering Shortcut Learning from an Evolutionary Game Theory Perspective

Shortcut learning causes deep learning models to rely on non-essential features within the data. However, its formation in deep neural network training still lacks theoretical understanding. In this paper, we provide a formal definition of core and shortcut features and employ evolutionary game theory to analyze the origins of shortcut bias by modeling data samples as players and their corresponding neural tangent features as strategies, assuming the existence of core and shortcut subnetworks. We find that gradient descent (GD) and stochastic gradient descent (SGD) lead to two distinct stochastically stable states, each corresponding to a different strategy. The former primarily optimizes the shortcut subnetwork, while the latter primarily optimizes the core subnetwork. We investigate the influence of these strategies on shortcut bias through a continuous stochastic differential equation, and reveal the impact of data noise and optimization noise on the formation of shortcut bias. In brief, our work employs evolutionary game theory to characterize the dynamics of shortcut bias formation and provides a theoretical view on its mitigation.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Information-theoretic Classification Accuracy: A Criterion that Guides Data-driven Combination of Ambiguous Outcome Labels in Multi-class Classification

Outcome labeling ambiguity and subjectivity are ubiquitous in real-world datasets. While practitioners commonly combine ambiguous outcome labels for all data points (instances) in an ad hoc way to improve the accuracy of multi-class classification, there lacks a principled approach to guide the label combination for all data points by any optimality criterion. To address this problem, we propose the information-theoretic classification accuracy (ITCA), a criterion that balances the trade-off between prediction accuracy (how well do predicted labels agree with actual labels) and classification resolution (how many labels are predictable), to guide practitioners on how to combine ambiguous outcome labels. To find the optimal label combination indicated by ITCA, we propose two search strategies: greedy search and breadth-first search. Notably, ITCA and the two search strategies are adaptive to all machine-learning classification algorithms. Coupled with a classification algorithm and a search strategy, ITCA has two uses: improving prediction accuracy and identifying ambiguous labels. We first verify that ITCA achieves high accuracy with both search strategies in finding the correct label combinations on synthetic and real data. Then we demonstrate the effectiveness of ITCA in diverse applications including medical prognosis, cancer survival prediction, user demographics prediction, and cell type classification. We also provide theoretical insights into ITCA by studying the oracle and the linear discriminant analysis classification algorithms. Python package itca (available at https://github.com/JSB-UCLA/ITCA) implements ITCA and search strategies.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

A Mathematical Principle of Deep Learning: Learn the Geodesic Curve in the Wasserstein Space

Recent studies revealed the mathematical connection of deep neural network (DNN) and dynamic system. However, the fundamental principle of DNN has not been fully characterized with dynamic system in terms of optimization and generalization. To this end, we build the connection of DNN and continuity equation where the measure is conserved to model the forward propagation process of DNN which has not been addressed before. DNN learns the transformation of the input distribution to the output one. However, in the measure space, there are infinite curves connecting two distributions. Which one can lead to good optimization and generaliztion for DNN? By diving the optimal transport theory, we find DNN with weight decay attempts to learn the geodesic curve in the Wasserstein space, which is induced by the optimal transport map. Compared with plain network, ResNet is a better approximation to the geodesic curve, which explains why ResNet can be optimized and generalize better. Numerical experiments show that the data tracks of both plain network and ResNet tend to be line-shape in term of line-shape score (LSS), and the map learned by ResNet is closer to the optimal transport map in term of optimal transport score (OTS). In a word, we conclude a mathematical principle of deep learning is to learn the geodesic curve in the Wasserstein space; and deep learning is a great engineering realization of continuous transformation in high-dimensional space.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Adversarial Information Bottleneck

The information bottleneck (IB) principle has been adopted to explain deep learning in terms of information compression and prediction, which are balanced by a trade-off hyperparameter. How to optimize the IB principle for better robustness and figure out the effects of compression through the trade-off hyperparameter are two challenging problems. Previous methods attempted to optimize the IB principle by introducing random noise into learning the representation and achieved state-of-the-art performance in the nuisance information compression and semantic information extraction. However, their performance on resisting adversarial perturbations is far less impressive. To this end, we propose an adversarial information bottleneck (AIB) method without any explicit assumptions about the underlying distribution of the representations, which can be optimized effectively by solving a Min-Max optimization problem. Numerical experiments on synthetic and real-world datasets demonstrate its effectiveness on learning more invariant representations and mitigating adversarial perturbations compared to several competing IB methods. In addition, we analyse the adversarial robustness of diverse IB methods contrasting with their IB curves, and reveal that IB models with the hyperparameter $β$ corresponding to the knee point in the IB curve achieve the best trade-off between compression and prediction, and has best robustness against various attacks.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Matrix Normal PCA for Interpretable Dimension Reduction and Graphical Noise Modeling

Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of independent identical Gaussian noise. Probabilistic PCA (PPCA) and its variants have been extensively studied for decades. Most of them assume the underlying noise follows a certain independent identical distribution. However, the noise in the real world is usually complicated and structured. To address this challenge, some variants of PCA for data with non-IID noise have been proposed. However, most of the existing methods only assume that the noise is correlated in the feature space while there may exist two-way structured noise. To this end, we propose a powerful and intuitive PCA method (MN-PCA) through modeling the graphical noise by the matrix normal distribution, which enables us to explore the structure of noise in both the feature space and the sample space. MN-PCA obtains a low-rank representation of data and the structure of noise simultaneously. And it can be explained as approximating data over the generalized Mahalanobis distance. We develop two algorithms to solve this model: one maximizes the regularized likelihood, the other exploits the Wasserstein distance, which is more robust. Extensive experiments on various data demonstrate their effectiveness.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Tessellated Wasserstein Auto-Encoders

Non-adversarial generative models such as variational auto-encoder (VAE), Wasserstein auto-encoders with maximum mean discrepancy (WAE-MMD), sliced-Wasserstein auto-encoder (SWAE) are relatively easy to train and have less mode collapse compared to Wasserstein auto-encoder with generative adversarial network (WAE-GAN). However, they are not very accurate in approximating the target distribution in the latent space because they don't have a discriminator to detect the minor difference between real and fake. To this end, we develop a novel non-adversarial framework called Tessellated Wasserstein Auto-encoders (TWAE) to tessellate the support of the target distribution into a given number of regions by the centroidal Voronoi tessellation (CVT) technique and design batches of data according to the tessellation instead of random shuffling for accurate computation of discrepancy. Theoretically, we demonstrate that the error of estimate to the discrepancy decreases when the numbers of samples $n$ and regions $m$ of the tessellation become larger with rates of $\mathcal{O}(\frac{1}{\sqrt{n}})$ and $\mathcal{O}(\frac{1}{\sqrt{m}})$, respectively. Given fixed $n$ and $m$, a necessary condition for the upper bound of measurement error to be minimized is that the tessellation is the one determined by CVT. TWAE is very flexible to different non-adversarial metrics and can substantially enhance their generative performance in terms of Fréchet inception distance (FID) compared to VAE, WAE-MMD, SWAE. Moreover, numerical results indeed demonstrate that TWAE is competitive to the adversarial model WAE-GAN, demonstrating its powerful generative ability.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Distributed Bayesian Matrix Decomposition for Big Data Mining and Clustering

Matrix decomposition is one of the fundamental tools to discover knowledge from big data generated by modern applications. However, it is still inefficient or infeasible to process very big data using such a method in a single machine. Moreover, big data are often distributedly collected and stored on different machines. Thus, such data generally bear strong heterogeneous noise. It is essential and useful to develop distributed matrix decomposition for big data analytics. Such a method should scale up well, model the heterogeneous noise, and address the communication issue in a distributed system. To this end, we propose a distributed Bayesian matrix decomposition model (DBMD) for big data mining and clustering. Specifically, we adopt three strategies to implement the distributed computing including 1) the accelerated gradient descent, 2) the alternating direction method of multipliers (ADMM), and 3) the statistical inference. We investigate the theoretical convergence behaviors of these algorithms. To address the heterogeneity of the noise, we propose an optimal plug-in weighted average that reduces the variance of the estimation. Synthetic experiments validate our theoretical results, and real-world experiments show that our algorithms scale up well to big data and achieves superior or competing performance compared to other distributed methods.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Towards Understanding Residual and Dilated Dense Neural Networks via Convolutional Sparse Coding

Convolutional neural network (CNN) and its variants have led to many state-of-art results in various fields. However, a clear theoretical understanding about them is still lacking. Recently, multi-layer convolutional sparse coding (ML-CSC) has been proposed and proved to equal such simply stacked networks (plain networks). Here, we think three factors in each layer of it including the initialization, the dictionary design and the number of iterations greatly affect the performance of ML-CSC. Inspired by these considerations, we propose two novel multi-layer models--residual convolutional sparse coding model (Res-CSC) and mixed-scale dense convolutional sparse coding model (MSD-CSC), which have close relationship with the residual neural network (ResNet) and mixed-scale (dilated) dense neural network (MSDNet), respectively. Mathematically, we derive the shortcut connection in ResNet as a special case of a new forward propagation rule on ML-CSC. We find a theoretical interpretation of the dilated convolution and dense connection in MSDNet by analyzing MSD-CSC, which gives a clear mathematical understanding about them. We implement the iterative soft thresholding algorithm (ISTA) and its fast version to solve Res-CSC and MSD-CSC, which can employ the unfolding operation for further improvements. At last, extensive numerical experiments and comparison with competing methods demonstrate their effectiveness using three typical datasets.

0 citations0 reviewsNo code linkedOpen access