报告题目：Concentration of Measure Bounds for Matrix-variate Data with Missing Values
报 告 人： Shuheng Zhou
报告时间：2023年8月28日(周一) 14:00
报告地点：中国科学院大学中关村校区教学楼N513
内容摘要
We consider the following data perturbation model, where the covariates incur multiplicative errors. For two random matrices U, X, we denote by (U \circ X) the Hadamard or Schur product, which is defined as (U \circ X)_{i,j} = (U_{i,j}) (X_{ij}). In this paper, we study the subgaussian matrix variate model, where we observe the matrix variate data through a random mask U: \mathcal{X} = U \circ X, where X = B^{1/2} Z A^{1/2}, where Z is a random matrix with independent subgaussian entries, and U is a mask matrix with either zero or positive entries, where $E[U_{ij] \in [0,1]$ and all entries are mutually independent.Under the assumption of independence between X and U, we introduce componentwise unbiased estimators for estimating covariance A and B, and prove the concentration of measure bounds in the sense of guaranteeing the restricted eigenvalue(RE) conditions to hold on the unbiased estimator for B, when columns of data matrix are sampled with different rates. We further develop multiple regression methods for estimating the inverse of B and show statistical rate of convergence. Our results provide insight for sparse recovery for relationships among entities (samples, locations, items) when features (variables, time points, user ratings) are present in the observed data matrix X with heterogeneous rates. Our proof techniques can certainly be extended to other scenarios. We provide simulation evidence illuminating the theoretical predictions.
主讲人简介
Shuheng Zhou did her doctoral work in theoretical computer science, focusing on randomized and approximation algorithms. She subsequently earned a Ph.D. in Computer and Electrical Engineering from Carnegie Mellon University. She stayed at CMU for her first postdoc before moving to ETH Zurich for 18 months. She accepted her current position at the University of California, Riverside as a tenured associate professor in October 2017, and began her appointment in July 2018.
