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Zongming Ma

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9 papers

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NeurIPS Conference 2025 Conference Paper

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables

Yu Gui
Cong Ma
Zongming Ma

Multi-modal contrastive learning as a self-supervised representation learning technique has achieved great success in foundation model training, such as CLIP~\citep{radford2021learning}. In this paper, we study the theoretical properties of the learned representations from multi-modal contrastive learning beyond linear representations and specific data distributions. Our analysis reveals that, enabled by temperature optimization, multi-modal contrastive learning not only maximizes mutual information between modalities but also adapts to intrinsic dimensions of data, which can be much lower than user-specified dimensions for representation vectors. Experiments on both synthetic and real-world datasets demonstrate the ability of contrastive learning to learn low-dimensional and informative representations, bridging theoretical insights and practical performance.

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JMLR Journal 2023 Journal Article

Sparse GCA and Thresholded Gradient Descent

Sheng Gao
Zongming Ma

Generalized correlation analysis (GCA) is concerned with uncovering linear relationships across multiple data sets. It generalizes canonical correlation analysis that is designed for two data sets. We study sparse GCA when there are potentially multiple leading generalized correlation tuples in data that are of interest and the loading matrix has a small number of nonzero rows. It includes sparse CCA and sparse PCA of correlation matrices as special cases. We first formulate sparse GCA as a generalized eigenvalue problem at both population and sample levels via a careful choice of normalization constraints. Based on a Lagrangian form of the sample optimization problem, we propose a thresholded gradient descent algorithm for estimating GCA loading vectors and matrices in high dimensions. We derive tight estimation error bounds for estimators generated by the algorithm with proper initialization. We also demonstrate the prowess of the algorithm on a number of synthetic data sets. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

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JMLR Journal 2022 Journal Article

Community detection in sparse latent space models

Fengnan Gao
Zongming Ma
Hongsong Yuan

We show that a simple community detection algorithm originated from stochastic blockmodel literature achieves consistency, and even optimality, for a broad and flexible class of sparse latent space models. The class of models includes latent eigenmodels (Hoff, 2008). The community detection algorithm is based on spectral clustering followed by local refinement via normalized edge counting. It is easy to implement and attains high accuracy with a low computational budget. The proof of its optimality depends on a neat equivalence between likelihood ratio test and edge counting in a simple vs. simple hypothesis testing problem that underpins the refinement step, which could be of independent interest. [abs] [ pdf ][ bib ] &copy JMLR 2022. ( edit, beta )

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JMLR Journal 2022 Journal Article

Nonconvex Matrix Completion with Linearly Parameterized Factors

Ji Chen
Xiaodong Li
Zongming Ma

Techniques of matrix completion aim to impute a large portion of missing entries in a data matrix through a small portion of observed ones. In practice, prior information and special structures are usually employed in order to improve the accuracy of matrix completion. In this paper, we propose a unified nonconvex optimization framework for matrix completion with linearly parameterized factors. In particular, by introducing a condition referred to as Correlated Parametric Factorization, we conduct a unified geometric analysis for the nonconvex objective by establishing uniform upper bounds for low-rank estimation resulting from any local minimizer. Perhaps surprisingly, the condition of Correlated Parametric Factorization holds for important examples including subspace-constrained matrix completion and skew-symmetric matrix completion. The effectiveness of our unified nonconvex optimization method is also empirically illustrated by extensive numerical simulations. [abs] [ pdf ][ bib ] &copy JMLR 2022. ( edit, beta )

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JMLR Journal 2020 Journal Article

Universal Latent Space Model Fitting for Large Networks with Edge Covariates

Zhuang Ma
Zongming Ma
Hongsong Yuan

Latent space models are effective tools for statistical modeling and visualization of network data. Due to their close connection to generalized linear models, it is also natural to incorporate covariate information in them. The current paper presents two universal fitting algorithms for networks with edge covariates: one based on nuclear norm penalization and the other based on projected gradient descent. Both algorithms are motivated by maximizing the likelihood function for an existing class of inner-product models, and we establish their statistical rates of convergence for these models. In addition, the theory informs us that both methods work simultaneously for a wide range of different latent space models that allow latent positions to affect edge formation in flexible ways, such as distance models. Furthermore, the effectiveness of the methods is demonstrated on a number of real world network data sets for different statistical tasks, including community detection with and without edge covariates, and network assisted learning. [abs] [ pdf ][ bib ] &copy JMLR 2020. ( edit, beta )

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JMLR Journal 2017 Journal Article

Achieving Optimal Misclassification Proportion in Stochastic Block Models

Chao Gao
Zongming Ma
Anderson Y. Zhang
Harrison H. Zhou

Community detection is a fundamental statistical problem in network data analysis. In this paper, we present a polynomial time two-stage method that provably achieves optimal statistical performance in misclassification proportion for stochastic block model under weak regularity conditions. Our two-stage procedure consists of a refinement stage motivated by penalized local maximum likelihood estimation. This stage can take a wide range of weakly consistent community detection procedures as its initializer, to which it applies and outputs a community assignment that achieves optimal misclassification proportion with high probability. The theoretical property is confirmed by simulated examples. [abs] [ pdf ][ bib ] &copy JMLR 2017. ( edit, beta )

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JMLR Journal 2016 Journal Article

Optimal Estimation and Completion of Matrices with Biclustering Structures

Chao Gao
Yu Lu
Zongming Ma
Harrison H. Zhou

Biclustering structures in data matrices were first formalized in a seminal paper by John Hartigan (Hartigan, 1972) where one seeks to cluster cases and variables simultaneously. Such structures are also prevalent in block modeling of networks. In this paper, we develop a theory for the estimation and completion of matrices with biclustering structures, where the data is a partially observed and noise contaminated matrix with a certain underlying biclustering structure. In particular, we show that a constrained least squares estimator achieves minimax rate-optimal performance in several of the most important scenarios. To this end, we derive unified high probability upper bounds for all sub-Gaussian data and also provide matching minimax lower bounds in both Gaussian and binary cases. Due to the close connection of graphon to stochastic block models, an immediate consequence of our general results is a minimax rate- optimal estimator for sparse graphons. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

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JMLR Journal 2016 Journal Article

Rate Optimal Denoising of Simultaneously Sparse and Low Rank Matrices

Dan Yang
Zongming Ma
Andreas Buja

We study minimax rates for denoising simultaneously sparse and low rank matrices in high dimensions. We show that an iterative thresholding algorithm achieves (near) optimal rates adaptively under mild conditions for a large class of loss functions. Numerical experiments on synthetic datasets also demonstrate the competitive performance of the proposed method. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

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JMLR Journal 2008 Journal Article

Structural Learning of Chain Graphs via Decomposition

Zongming Ma
Xianchao Xie
Zhi Geng

Chain graphs present a broad class of graphical models for description of conditional independence structures, including both Markov networks and Bayesian networks as special cases. In this paper, we propose a computationally feasible method for the structural learning of chain graphs based on the idea of decomposing the learning problem into a set of smaller scale problems on its decomposed subgraphs. The decomposition requires conditional independencies but does not require the separators to be complete subgraphs. Algorithms for both skeleton recovery and complex arrow orientation are presented. Simulations under a variety of settings demonstrate the competitive performance of our method, especially when the underlying graph is sparse. [abs] [ pdf ][ bib ] &copy JMLR 2008. ( edit, beta )

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