Connections Between Minimal Norm Interpolation and Local Theory of Banach Spaces

Explore the statistical performance of minimum norm interpolators in non-linear regression with additive Gaussian noise in this 32-minute lecture by Gil Kur at the Hausdorff Center for Mathematics. Focus on norms satisfying 2-uniformly convexity or the cotype 2 property, including inner-product spaces, ℓp norms, and Wp Sobolev spaces for 1 ≤ p ≤ 2. Discover the main result showing that under 2-uniform convexity, the bias of the minimal norm solution is bounded by the Gaussian complexity of the class. Learn about an Efron-Stein type estimate for the variance of the minimal norm solution under cotype 2 or 2-uniform convexity. Gain insights into the novel approach leveraging tools from the local theory of infinite dimensional Banach spaces, which is the first to study non-linear models that are "far" from Hilbert spaces.