Gaussian Comparison for High-Dimensional Inference: Statistical Limits and Algorithmic Dynamics
GALEN REEVES – DUKE UNIVERSITY
ABSTRACT
Gaussian comparison models connect statistical limits and algorithmic performance across high-dimensional inference problems, including networks, spiked matrices, and regression. I will introduce this perspective through the matrix tensor product model, tracing its origins in recovering latent structure from multiple networks and covariate information.
The talk then addresses two questions about the accuracy and reach of these Gaussian predictions. First, how well do they describe finite-sample algorithmic dynamics? I will present an explicit coupling approach that provides non-asymptotic control of approximate message passing (AMP) and more general first-order methods. Second, when do Gaussian statistical predictions extend to non-Gaussian observations? I will discuss recent joint work with Wenxuan Zou establishing Gaussian comparisons of posterior estimation error and uncertainty that accommodate model mismatch and apply to sparse networks.