A vector-contraction inequality for Rademacher complexities using $p$-stable variables

TL;DR

This paper extends the vector-contraction inequality for Rademacher complexities by incorporating p-stable variables, broadening the scope of the original inequality to include a wider class of stable distributions.

Contribution

The work generalizes Maurer's vector-contraction inequality from sub-gaussian to p-stable variables, enabling new applications in complexity analysis.

Findings

Extended the contraction inequality to p-stable variables for 1<p<2

Provided theoretical bounds for Rademacher complexities with p-stable variables

Broadened the applicability of contraction inequalities in learning theory

Abstract

Andreas Maurer in the paper "A vector-contraction inequality for Rademacher complexities" extended the contraction inequality for Rademacher averages to Lipschitz functions with vector-valued domains; He did it replacing the Rademacher variables in the bounding expression by arbitrary idd symmetric and sub-gaussian variables. We will see how to extend this work when we replace sub-gaussian variables by $p$-stable variables for $1<p<2$.