arXiv subjects

Zeng Li

Publications and source records attributed to Zeng Li.

At least 19 recordsLinked to original sources

arXiv2026

Features Extraction Across Multi-Source Heterogeneous Data

High-dimensional data from multiple sources often combine shared structure with source-specific variation. We study heterogeneous principal component analysis, which seeks to recover common and private principal subspaces when their dimensions are unknown. {We propose \emph{Feature Extraction (FE)}, a novel data-driven framework with two steps. First, the Eigenvector-based Spike-Count (ESC) estimator determines the number of principal components (PC) in each source using only sample eigenvector information, rather than eigenvalue-based criteria. Second, FE identifies the locations of common features by comparing bias-corrected inner products between sample eigenvectors across sources. These matches yield estimates of the common and source-specific subspaces without iterative optimization. We establish the consistency of our estimators under a spiked covariance model in a high-dimensional regime where the dimension and sample size grow proportionally. Simulations and applications to federated image data and U.S. housing prices demonstrate the performance of FE in rank recovery, subspace estimation, and data reconstruction.} Code is available at https://github.com/liwenbo-research/HeterogeneousPCA

stat.ME↗

arXiv2026

On Eigenvector Statistics of Large-Dimensional Sample Covariance Matrices with Applications

We study the eigenvector-weighted spectral statistics \[ T_n(φ,g)=p^{-1}tr\{φ(\boldsymbol{S}_n)g(\boldsymbolΣ)\} \] of large-dimensional sample covariance matrices $\boldsymbol{S}_n$ with population covariance $\boldsymbolΣ$. These statistics combine functions of sample eigenvalues with sample--population eigenvector overlaps and arise in statistical losses that depend on both. As the dimension and sample size grow proportionally, we establish a joint central limit theorem for $\{T_n(φ_a,g_a)\}_{a=1}^r$ with multiple analytic test functions and population weights, centered by finite-dimensional deterministic equivalents. A key intermediate step is a joint Gaussian process limit for the weighted resolvent traces \[ m_n^g(z)=p^{-1}tr\{(\boldsymbol{S}_n-z\boldsymbol{I}_p)^{-1}g(\boldsymbolΣ)\}. \] The limiting means and cross-covariances are expressed in terms of the population spectral distribution. We apply these results in two settings: one concerns the variance component of minimum-norm prediction risk, and the other concerns the Frobenius loss of fixed rotationally invariant covariance estimators. For fixed affine shrinkage rules, the loss means, variances, and cross-covariances have explicit formulas in terms of population spectral moments.

math.ST↗

arXiv2026

Mean-Shift PCA by Knockoff Mean

Removing noise is difficult, but adding noise is easy. In this work, we show how to eliminate mean-shift noisy components from PCA by deliberately introducing knockoff mean-shift perturbation. Standard PCA is highly sensitive to shifts in the sample mean: a small fraction of samples from a shifted distribution can cause large deviations in the leading principal components. In high-dimensional regimes, existing Robust PCA approaches cannot handle the mean-shift contamination structure inherent in the mixture model. Using tools from Random Matrix Theory, we prove that the mean-shift spikes are spectrally separable from the stable eigenvalues of the original covariance. Furthermore, the original eigenspace remains asymptotically invariant to the contamination, independent of the mixture weight. Exploiting this spectral stability, we propose a simple, two-stage PCA algorithm by adding knockoff mean that identifies and removes the mean-shift component using only standard PCA operations.

stat.ML↗

arXiv2026

Masked Next-Scale Prediction for Self-supervised Scene Text Recognition

Scene Text Recognition requires modeling visual structures that evolve from coarse layouts to fine-grained character strokes. Training such models relies on large amounts of annotated data. Recent self-supervised approaches, such as Masked Image Modeling (MIM), alleviate this dependency by leveraging large-scale unlabeled data. Yet most existing MIM methods operate at a single spatial scale and fail to capture the hierarchical nature of scene text. In this work, we introduce Masked Next-Scale Prediction (MNSP), a unified self-supervised framework designed to explicitly model cross-scale structural evolution. The framework incorporates Next-Scale Prediction (NSP), which learns hierarchical representations by predicting higher-resolution features from lower-resolution contexts. Naive scale prediction, however, tends to produce spatially diffuse attention, directing the model toward background regions rather than textual structures. MNSP resolves this limitation by jointly learning cross-scale prediction and masked image reconstruction. NSP captures global layout priors across resolutions, while masked reconstruction imposes strong local constraints that guide attention toward informative text regions. A Multi-scale Linguistic Alignment module further maintains semantic consistency across different resolutions. Extensive experiments demonstrate that MNSP achieves state-of-the-art performance, reaching 86.2\% average accuracy on the challenging Union14M benchmark and 96.7\% across six standard datasets. Additional analyses show that our method improves robustness under extreme scale and layout variations. Code is available at https://github.com/CzhczhcHczh/MNSP

cs.CV↗

arXiv2025

Orbit-Controlled Generation of Two-color Attosecond Mode-locked Free-electron Lasers

The generation of attosecond X-ray pulses has garnered significant attention within the X-ray free-electron laser (FEL) community due to their potential for ultrafast time-resolved studies. Such pulses enable the investigation of electron dynamics with unprecedented temporal resolution, opening new avenues in fields such as quantum control and ultrafast spectroscopy. In an FEL, the mode-locking technique synthesizes a comb of longitudinal modes by applying spatiotemporal shifts between the co-propagating radiation and the electron bunch. Here, we propose a novel scheme for generating two-color attosecond mode-locked FEL pulses via orbit control in two-stage mode-locked undulators. Specifically, a chicane with a wiggler inserted in the middle generates periodic temporal-transverse modulation in the electron beam. In this configuration, the low-energy and high-energy components of the beam lase in separate undulator sections, with each producing attosecond mode-locked FEL pulses. Three-dimensional simulations with realistic parameters confirm that trains of 250-attosecond soft X-ray pulses at the gigawatt level can be independently generated in each undulator section. Furthermore, time delay between the two pulse trains can be adjusted over a range of several hundred femtoseconds.

physics.acc-ph↗

arXiv2025

A Multi-Store Privacy Measurement of Virtual Reality App Ecosystem

Virtual Reality (VR) has gained increasing traction among various domains in recent years, with major companies such as Meta, Pico, and Microsoft launching their application stores to support third-party developers in releasing their applications (or simply apps). These apps offer rich functionality but inherently collect privacy-sensitive data, such as user biometrics, behaviors, and the surrounding environment. Nevertheless, there is still a lack of domain-specific regulations to govern the data handling of VR apps, resulting in significant variations in their privacy practices among app stores. In this work, we present the first comprehensive multi-store study of privacy practices in the current VR app ecosystem, covering a large-scale dataset involving 6,565 apps collected from five major app stores. We assess both declarative and behavioral privacy practices of VR apps, using a multi-faceted approach based on natural language processing, reverse engineering, and static analysis. Our assessment reveals significant privacy compliance issues across all stores, underscoring the premature status of privacy protection in this rapidly growing ecosystem. For instance, one third of apps fail to declare their use of sensitive data, and 21.5\% of apps neglect to provide valid privacy policies. Our work sheds light on the status quo of privacy protection within the VR app ecosystem for the first time. Our findings should raise an alert to VR app developers and users, and encourage store operators to implement stringent regulations on privacy compliance among VR apps.

cs.CR↗

arXiv2025

Debiased distributed PCA under high dimensional spiked model

We study distributed principal component analysis (PCA) in high-dimensional settings under the spiked model. In such regimes, sample eigenvectors can deviate significantly from population ones, introducing a persistent bias. Existing distributed PCA methods are sensitive to this bias, particularly when the number of machines is small. Their consistency typically relies on the number of machines tending to infinity. We propose a debiased distributed PCA algorithm that corrects the local bias before aggregation and incorporates a sparsity-detection step to adaptively handle sparse and non-sparse eigenvectors. Theoretically, we establish the consistency of our estimator under much weaker conditions compared to existing literature. In particular, our approach does not require symmetric innovations and only assumes a finite sixth moment. Furthermore, our method generally achieves smaller estimation error, especially when the number of machines is small. Empirically, extensive simulations and real data experiments demonstrate that our method consistently outperforms existing distributed PCA approaches. The advantage is especially prominent when the leading eigenvectors are sparse or the number of machines is limited. Our method and theoretical analysis are also applicable to the sample correlation matrix.

stat.ME↗

arXiv2025

On eigenvalues of a renormalized sample correlation matrix

This paper studies the asymptotic spectral properties of a renormalized sample correlation matrix, including the limiting spectral distribution, the properties of largest eigenvalues, and the central limit theorem for linear spectral statistics. All asymptotic results are derived under a unified framework where the dimension-to-sample size ratio $p/n\rightarrow c\in (0,\infty]$. Based on our CLT result, we propose an independence test statistic capable of operating effectively in both high and ultrahigh dimensional scenarios. Simulation experiments demonstrate the accuracy of theoretical results.

math.ST↗

arXiv2024

On spiked eigenvalues of a renormalized sample covariance matrix from multi-population

Sample covariance matrices from multi-population typically exhibit several large spiked eigenvalues, which stem from differences between population means and are crucial for inference on the underlying data structure. This paper investigates the asymptotic properties of spiked eigenvalues of a renormalized sample covariance matrices from multi-population in the ultrahigh dimensional context where the dimension-to-sample size ratio p/n go to infinity. The first- and second-order convergence of these spikes are established based on asymptotic properties of three types of sesquilinear forms from multi-population. These findings are further applied to two scenarios,including determination of total number of subgroups and a new criterion for evaluating clustering results in the absence of true labels. Additionally, we provide a unified framework with p/n->c\in (0,\infty] that integrates the asymptotic results in both high and ultrahigh dimensional settings.

math.ST↗

arXiv2024

Robust estimation for number of factors in high dimensional factor modeling via Spearman correlation matrix

Determining the number of factors in high-dimensional factor modeling is essential but challenging, especially when the data are heavy-tailed. In this paper, we introduce a new estimator based on the spectral properties of Spearman sample correlation matrix under the high-dimensional setting, where both dimension and sample size tend to infinity proportionally. Our estimator is robust against heavy tails in either the common factors or idiosyncratic errors. The consistency of our estimator is established under mild conditions. Numerical experiments demonstrate the superiority of our estimator compared to existing methods.

stat.ME↗

arXiv2024

On testing mean of high dimensional compositional data

We investigate one/two-sample mean tests for high-dimensional compositional data when the number of variables is comparable with the sample size, as commonly encountered in microbiome research. Existing methods mainly focus on max-type test statistics which are suitable for detecting sparse signals. However, in this paper, we introduce a novel approach using sum-type test statistics which are capable of detecting weak but dense signals. By establishing the asymptotic independence between the max-type and sum-type test statistics, we further propose a combined max-sum type test to cover both cases. We derived the asymptotic null distributions and power functions for these test statistics. Simulation studies demonstrate the superiority of our max-sum type test statistics which exhibit robust performance regardless of data sparsity.

math.ST↗

arXiv2024

TextBlockV2: Towards Precise-Detection-Free Scene Text Spotting with Pre-trained Language Model

Existing scene text spotters are designed to locate and transcribe texts from images. However, it is challenging for a spotter to achieve precise detection and recognition of scene texts simultaneously. Inspired by the glimpse-focus spotting pipeline of human beings and impressive performances of Pre-trained Language Models (PLMs) on visual tasks, we ask: 1) "Can machines spot texts without precise detection just like human beings?", and if yes, 2) "Is text block another alternative for scene text spotting other than word or character?" To this end, our proposed scene text spotter leverages advanced PLMs to enhance performance without fine-grained detection. Specifically, we first use a simple detector for block-level text detection to obtain rough positional information. Then, we finetune a PLM using a large-scale OCR dataset to achieve accurate recognition. Benefiting from the comprehensive language knowledge gained during the pre-training phase, the PLM-based recognition module effectively handles complex scenarios, including multi-line, reversed, occluded, and incomplete-detection texts. Taking advantage of the fine-tuned language model on scene recognition benchmarks and the paradigm of text block detection, extensive experiments demonstrate the superior performance of our scene text spotter across multiple public benchmarks. Additionally, we attempt to spot texts directly from an entire scene image to demonstrate the potential of PLMs, even Large Language Models (LLMs).

cs.CV↗

arXiv2023

On eigenvalues of sample covariance matrices based on high dimensional compositional data

This paper studies the asymptotic spectral properties of the sample covariance matrix for high dimensional compositional data, including the limiting spectral distribution, the limit of extreme eigenvalues, and the central limit theorem for linear spectral statistics. All asymptotic results are derived under the high-dimensional regime where the data dimension increases to infinity proportionally with the sample size. The findings reveal that the limiting spectral distribution is the well-known Marchenko-Pastur law. The largest (or smallest non-zero) eigenvalue converges almost surely to the left (or right) endpoint of the limiting spectral distribution, respectively. Moreover, the linear spectral statistics demonstrate a Gaussian limit. Simulation experiments demonstrate the accuracy of theoretical results.

math.ST↗

arXiv2023

Heavy-Tailed Regularization of Weight Matrices in Deep Neural Networks

Unraveling the reasons behind the remarkable success and exceptional generalization capabilities of deep neural networks presents a formidable challenge. Recent insights from random matrix theory, specifically those concerning the spectral analysis of weight matrices in deep neural networks, offer valuable clues to address this issue. A key finding indicates that the generalization performance of a neural network is associated with the degree of heavy tails in the spectrum of its weight matrices. To capitalize on this discovery, we introduce a novel regularization technique, termed Heavy-Tailed Regularization, which explicitly promotes a more heavy-tailed spectrum in the weight matrix through regularization. Firstly, we employ the Weighted Alpha and Stable Rank as penalty terms, both of which are differentiable, enabling the direct calculation of their gradients. To circumvent over-regularization, we introduce two variations of the penalty function. Then, adopting a Bayesian statistics perspective and leveraging knowledge from random matrices, we develop two novel heavy-tailed regularization methods, utilizing Powerlaw distribution and Frechet distribution as priors for the global spectrum and maximum eigenvalues, respectively. We empirically show that heavytailed regularization outperforms conventional regularization techniques in terms of generalization performance.

stat.ML↗

arXiv2023

Network Autoregression for Incomplete Matrix-Valued Time Series

We study the dynamics of matrix-valued time series with observed network structures by proposing a matrix network autoregression model with row and column networks of the subjects. We incorporate covariate information and a low rank intercept matrix. We allow incomplete observations in the matrices and the missing mechanism can be covariate dependent. To estimate the model, a two-step estimation procedure is proposed. The first step aims to estimate the network autoregression coefficients, and the second step aims to estimate the regression parameters, which are matrices themselves. Theoretically, we first separately establish the asymptotic properties of the autoregression coefficients and the error bounds of the regression parameters. Subsequently, a bias reduction procedure is proposed to reduce the asymptotic bias and the theoretical property of the debiased estimator is studied. Lastly, we illustrate the usefulness of the proposed method through a number of numerical studies and an analysis of a Yelp data set.

stat.ME↗

arXiv2022

On eigenvalues of a high-dimensional Kendall's rank correlation matrix with dependence

This paper investigates limiting spectral distribution of a high-dimensional Kendall's rank correlation matrix. The underlying population is allowed to have general dependence structure. The result no longer follows the generalized Marucenko-Pastur law, which is brand new. It's the first result on rank correlation matrices with dependence. As applications, we study the Kendall's rank correlation matrix for multivariate normal distributions with a general covariance matrix. From these results, we further gain insights on Kendall's rank correlation matrix and its connections with the sample covariance/correlation matrix.

math.ST↗

arXiv2022

Self-Constrained Inference Optimization on Structural Groups for Human Pose Estimation

We observe that human poses exhibit strong group-wise structural correlation and spatial coupling between keypoints due to the biological constraints of different body parts. This group-wise structural correlation can be explored to improve the accuracy and robustness of human pose estimation. In this work, we develop a self-constrained prediction-verification network to characterize and learn the structural correlation between keypoints during training. During the inference stage, the feedback information from the verification network allows us to perform further optimization of pose prediction, which significantly improves the performance of human pose estimation. Specifically, we partition the keypoints into groups according to the biological structure of human body. Within each group, the keypoints are further partitioned into two subsets, high-confidence base keypoints and low-confidence terminal keypoints. We develop a self-constrained prediction-verification network to perform forward and backward predictions between these keypoint subsets. One fundamental challenge in pose estimation, as well as in generic prediction tasks, is that there is no mechanism for us to verify if the obtained pose estimation or prediction results are accurate or not, since the ground truth is not available. Once successfully learned, the verification network serves as an accuracy verification module for the forward pose prediction. During the inference stage, it can be used to guide the local optimization of the pose estimation results of low-confidence keypoints with the self-constrained loss on high-confidence keypoints as the objective function. Our extensive experimental results on benchmark MS COCO and CrowdPose datasets demonstrate that the proposed method can significantly improve the pose estimation results.

cs.CV↗

arXiv2022

On singular values of large dimensional lag-tau sample autocorrelation matrices

We study the limiting behavior of singular values of a lag-$τ$ sample auto-correlation matrix $\bf{R}_τ^ε$ of error term $ε$ in the high-dimensional factor model. We establish the limiting spectral distribution (LSD) which characterizes the global spectrum of $\bf{R}_τ^ε$, and derive the limit of its largest singular value. All the asymptotic results are derived under the high-dimensional asymptotic regime where the data dimension and sample size go to infinity proportionally. Under mild assumptions, we show that the LSD of $\bf{R}_τ^ε$ is the same as that of the lag-$τ$ sample auto-covariance matrix. Based on this asymptotic equivalence, we additionally show that the largest singular value of $\bf{R}_τ^ε$ converges almost surely to the right end point of the support of its LSD. Our results take the first step to identify the number of factors in factor analysis using lag-$τ$ sample auto-correlation matrices. Our theoretical results are fully supported by numerical experiments as well.

math.ST↗