Stat Cafe - Mohsen Pourahmadi

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An Overview of High-Dimensional Covariance Estimation

Time: Monday 2/24/2025 from 11:30 AM to 12:30 PM
Location: BLOC 457
Food from Potbelly provided

Description

Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. We provide an overview of the progress made in modeling covariance matrices from two relatively complementary perspectives: (1) generalized linear models (GLM) or parsimony and use of covariates in low dimensions, and (2) regularization or sparsity for high-dimensional data. An emerging trend in both perspectives is that of reducing a covariance estimation problem to that of estimating a sequence of regression problems. The role of Cholesky decomposition in providing an unconstrained and statistically interpretable reparameterization which guarantees the positive-definiteness of the estimated covariance matrix will be highlighted. It reduces the unintuitive task of covariance estimation to that of modeling a sequence of regressions, but imposes an a priori order among the variables.