Covariance Estimation for Matrix-Variate Data with Missing Values and Mean Structure

• Activity Number: 215 - Contributed Poster Presentations: Section on Statistical Learning and Data Science
• Type: Contributed
• Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Roger Fan* and Shuheng Zhou and Byoungwook Jang
• Companies: University of Michigan and University of California, Riverside and University of Michigan
• Keywords: high-dimensional; covariance estimation; missing data; matrix-variate data; graphical model

Abstract

Modern complex data often involve dependencies among both axes of the data, which necessitates the development of methods and theory that are robust to non-independent data. One model that has sparked recent interest for these applications is the matrix-variate data model. At the same time, data are often incomplete with missing or corrupted values. In this work, we develop methods for estimating covariance and precision matrices in the presence of both dependence and missing values. Under sparsity and missing rate conditions, we show that our methods are able to estimate the covariance using a single random matrix from a matrix-variate distribution. We also develop modified methods for covariance estimation when unknown mean structure is additionally present. We establish consistency and obtain rates of convergence, as well as demonstrate the model's performance in simulation. We then use the proposed model to analyze U.S. Senate voting records from multiple Congresses. We document several structural changes over time, which are especially interesting considering that our datasets bracket the election of President Donald Trump in 2016, which many consider to have marked