arXiv subjects

Zhangni Pu

Publications and source records attributed to Zhangni Pu.

4 recordsLinked to original sources

arXiv2026

The Asymptotic Distribution of Sample Canonical Directions in Gaussian Spiked High-dimensional CCA

This paper studies the asymptotic behavior of sample canonical directions in a finite-rank spiked high-dimensional canonical correlation analysis model under a Gaussian population assumption. Under the asymptotic regime in which the dimensions of the two data blocks grow proportionally with the sample size, sample canonical directions are generally not consistent estimators of their population counterparts, even when the corresponding sample canonical correlations separate from the bulk spectrum. To quantify directional recovery, we investigate the squared alignment between a sample canonical direction and its associated population direction. For each simple population spike, we first establish a deterministic first-order limit for this squared alignment, which gives an explicit measure of the population-level directional information retained by the sample direction. We then prove a central limit theorem for its fluctuations around the deterministic limit, with an explicit asymptotic variance expressed through deterministic limits of resolvent trace functionals. To make the theoretical quantities computable from data, we further construct plug-in estimators for both the limiting mean and the asymptotic variance by inverting the deterministic outlier eigenvalue map, and prove their consistency. Numerical simulations and a real-data illustration support the theoretical results and demonstrate how the proposed estimators assess the recovery quality of sample canonical directions.

math.ST↗

arXiv2025

Structural Effect and Spectral Enhancement of High-Dimensional Regularized Linear Discriminant Analysis

Regularized linear discriminant analysis (RLDA) is a widely used tool for classification and dimensionality reduction, but its performance in high-dimensional scenarios is inconsistent. Existing theoretical analyses of RLDA often lack clear insight into how data structure affects classification performance. To address this issue, we derive a non-asymptotic approximation of the misclassification rate and thus analyze the structural effect and structural adjustment strategies of RLDA. Based on this, we propose the Spectral Enhanced Discriminant Analysis (SEDA) algorithm, which optimizes the data structure by adjusting the spiked eigenvalues of the population covariance matrix. By developing a new theoretical result on eigenvectors in random matrix theory, we derive an asymptotic approximation on the misclassification rate of SEDA. The bias correction algorithm and parameter selection strategy are then obtained. Experiments on synthetic and real datasets show that SEDA achieves higher classification accuracy and dimensionality reduction compared to existing LDA methods.

stat.ML↗

arXiv2024

The Asymptotic Properties of the Extreme Eigenvectors of High-dimensional Generalized Spiked Covariance Model

In this paper, we investigate the asymptotic behaviors of the extreme eigenvectors in a general spiked covariance matrix, where the dimension and sample size increase proportionally. We eliminate the restrictive assumption of the block diagonal structure in the population covariance matrix. Moreover, there is no requirement for the spiked eigenvalues and the 4th moment to be bounded. Specifically, we apply random matrix theory to derive the convergence and limiting distributions of certain projections of the extreme eigenvectors in a large sample covariance matrix within a generalized spiked population model. Furthermore, our techniques are robust and effective, even when spiked eigenvalues differ significantly in magnitude from nonspiked ones. Finally, we propose a powerful statistic for hypothesis testing for the eigenspaces of covariance matrices.

math.ST↗

arXiv2024

Spectrally-Corrected and Regularized Linear Discriminant Analysis for Spiked Covariance Model

This paper proposes an improved linear discriminant analysis called spectrally-corrected and regularized LDA (SRLDA). This method integrates the design ideas of the sample spectrally-corrected covariance matrix and the regularized discriminant analysis. With the support of a large-dimensional random matrix analysis framework, it is proved that SRLDA has a linear classification global optimal solution under the spiked model assumption. According to simulation data analysis, the SRLDA classifier performs better than RLDA and ILDA and is closer to the theoretical classifier. Experiments on different data sets show that the SRLDA algorithm performs better in classification and dimensionality reduction than currently used tools.

stat.ML↗