Sparsifying Suprema of Gaussian Processes

Explore a 49-minute lecture on approximating the supremum of centered Gaussian processes using finite-dimensional Gaussian processes. Delve into the proof that shows how the approximation's dimension depends solely on the target error. Discover the corollary demonstrating that for any norm Φ defined over R^n and target error ε, there exists a norm Ψ with specific properties related to dimensionality and probability. Examine the application of this concept to sparsifying high-dimensional polytopes in Gaussian space. Learn about the implications for computational learning and property testing. Understand the role of Talagrand's majorizing measures theorem in the proof. This talk, presented by Rocco Servedio at the Hausdorff Center for Mathematics, is based on joint work with Anindya De, Shivam Nadimpalli, and Ryan O'Donnell.