学术报告第114期

题目：Sparse Heteroskedastic PCA in High Dimensions

主讲人：匹兹堡大学统计系 任钊教授

主持人：西南财经大学统计与数据科学学院 常晋源教授

时间：2026年7月24日（周五）上午10:00-11:00

地点：西南财经大学光华校区光华楼1003会议室

报告摘要：

Principal component analysis (PCA) is one of the most commonly used techniques for dimension reduction and feature extraction. Though it has been well-studied for high-dimensional sparse PCA, little is known when the noise is heteroskedastic, which turns out to be ubiquitous in many scenarios. We propose an iterative algorithm, called SparseHPCA, for the sparse PCA problem in the presence of heteroskedastic noise, which alternatively updates the estimates of the sparse eigenvectors using orthogonal iteration with adaptive thresholdings in one step, and imputes the diagonal values of the sample covariance matrix to reduce the estimation bias due to heteroskedastic noise in the other step. Our procedure is computationally fast and provably optimal under the generalized spiked covariance model, assuming the leading eigenvectors are sparse. A comprehensive simulation study shows its robustness and effectiveness under various settings. The application of our new method to two high-dimensional genomics datasets, i.e., microarray and single-cell RNA sequencing (scRNA-seq) data, demonstrates its ability to preserve inherent cluster structures in downstream analyses. Additionally, we extend SparseHPCA to address the sparse singular value decomposition (sparse SVD) problem in the presence of heteroskedastic noise, further showcasing its versatility. If time permits, we will also discuss related statistical inference problems and extensions to estimation under differential privacy.

主讲人简介：

Prof. Zhao Ren received his Ph.D. in Statistics from Yale University in 2014. His research interests include high-dimensional statistical inference, robust inference, graphical models, nonparametric function estimation, and applications in statistical genomics.