PCA for High-Dimensional Heteroscedastic Data

Explore the challenges and solutions of applying Principal Component Analysis (PCA) to high-dimensional heteroscedastic data in this 40-minute conference talk by Laura Balzano from the University of Michigan. Delve into the limitations of classical PCA when dealing with heterogeneous datasets and discover how weighted PCA can improve the recovery of underlying subspaces. Learn about the optimal weighting strategies, asymptotic recovery expressions, and the surprising finding that inverse noise variance weighting is sub-optimal. Examine the Probabilistic PCA problem for heteroscedastic noise and its optimization techniques. Gain insights into cutting-edge research on dimensionality reduction for modern, high-dimensional applications combining diverse data sources.

Introduction
Motivation
Identifying Principal Components
Scaling PCA
High dimensional PCA
Optimal choice
Optimal weight
PCA
Results
Questions