Seminar: Statistical Learning in High Dimensions: From Computational Efficiency to Generalization Guarantees
By Mahsa Taheri

Mahsa Taheri will give a seminar on Friday 30/10 at 2pm on Zoom.

Statistical Learning in High Dimensions: From Computational Efficiency to Generalization Guarantees

Modern technologies generate increasingly complex, high-dimensional data, motivating learning methods that combine statistical guarantees with computational tractability. This talk examines the interplay between these two goals for regularized estimators in machine learning. In the first part, we introduce an adaptive validation approach that intertwines statistical guarantees with computational efficiency for estimators with convex losses. We then survey computationally efficient regularization methods in deep learning and the associated upper and lower bounds on generalization error. In the second part, we turn to diffusion models, focusing on challenges posed by high dimensionality, long inference times, and the strong global assumptions on the target density often required to establish convergence rates. We explore how incorporating the geometric structure of the data into the design of the diffusion process can yield faster contraction rates under mild local assumptions on the target density and improve performance on data with low intrinsic dimension. Together, these perspectives illustrate how regularization and data geometry can inform the design of statistically sound and computationally efficient learning methods.