Stat Cafe - Soham Ghosh
Posterior Contraction Rates for Subspace Estimation through Dense Factor Models
- Time: Tuesday 11/4/2025 from 11:10 AM to 12:25 PM
- Location: BLOC 448
Description
Principal Component Analysis (PCA) is a heavily used statistical tool for low-rank estimation and dimension reduction. Traditionally, some low-rank structure, like sparsity, is assumed for estimating PCs in high dimensions. However, very recently, consistent estimation of PCs has been established under the low effective rank assumption (re(Σ) = tr(Σ)/∥Σ∥, where tr denotes trace, ∥.∥ denotes operator norm). In this work, we propose a Bayesian method for estimating the principal subspace that achieves the frequentist optimal rate. Instead of assuming sparsity, we assume a relatively large signal-to-noise ratio, ensuring that the effective rank remains small. We use a very simple prior that facilitates the formulation of an efficient computational strategy.
Our Speaker
Soham Ghosh is a Ph.D. student in the Department of Statistics at Texas A&M University, where he is fortunate to be advised by Dr. Anirban Bhattacharya. He earned his undergraduate degree from the Indian Statistical Institute, Kolkata. His research interests lie in high-dimensional statistics, covariance estimation, and Bayesian theory, with applications to time series and functional data.