學(xué)術(shù)沙龍主題: Modeling and Learning on High-Dimensional Matrix-Variate Sequences
報告人: 張旭，華南師范大學(xué)優(yōu)聘副教授
報告時間: 2025年4月2日(周三)；上午10:30—12:00
報告地點：南校區(qū)網(wǎng)絡(luò)安全大樓 120 會議室
報告人簡介：張旭，華南師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院優(yōu)聘副教授，博士畢業(yè)于東北師范大學(xué)統(tǒng)計系。曾赴香港大學(xué)、香港理工大學(xué)從事博士后工作。研究方向包括網(wǎng)絡(luò)數(shù)據(jù)分析，張量/矩陣數(shù)據(jù)的統(tǒng)計建模與推斷。論文發(fā)表于Journal of the American Statistical Association, Statistica Sinica, Science China Mathematics等期刊。
報告摘要: We propose a new matrix factor model, named RaDFaM, which is strictly derived from the general rank decomposition and assumes a high-dimensional vector factor model structure for each basis vector. RaDFaM contributes a novel class of low-rank latent structures that trade off between signal intensity and dimension reduction from a tensor subspace perspective. Based on the intrinsic separable covariance structure of RaDFaM, for a collection of matrix-valued observations, we derive a new class of PCA variants for estimating loading matrices, and sequentially the latent factor matrices. The peak signal-to-noise ratio of RaDFaM is proved to be superior in the category of PCA-type estimators. We also establish an asymptotic theory including the consistency, convergence rates, and asymptotic distributions for components in the signal part. Numerically, we demonstrate the performance of RaDFaM in applications such as matrix reconstruction, supervised learning, and clustering, on uncorrelated and correlated data, respectively.
