Optimal Learning Rates for Regularized Least-Squares with a Fourier Capacity Condition

Wednesday, December 14, 2022 - 4:00pm to 4:30pm

Event Calendar Category

LIDS & Stats Tea

Speaker Name

Prem Murali Talwai



Building and Room Number

LIDS Lounge


We derive minimax adaptive rates for a new, broad class of Tikhonov-regularized learning problems in Hilbert scales under general source conditions. Our analysis does not require the regression function to be contained in the hypothesis class, and most notably does not employ the conventional a priori assumptions on kernel eigendecay. Using the theory of real interpolation, we demonstrate that the spectrum of the Mercer operator can be inferred in the presence of “tight” L∞ embeddings of suitable Hilbert scales. Our analysis utilizes a new Fourier capacity condition, which characterizes the optimal Lorentz range space of a modified Mercer operator in certain parameter regimes.


Prem Talwai is a third-year PhD student in the Operations Research Center and LIDS, advised by David Simchi-Levi. His interests lie at the intersection of harmonic analysis, probability, and learning theory, and its applications to operations management and finance. Previously, he completed his undergraduate studies in math at Cornell.

Arxiv link: https://arxiv.org/abs/2204.07856