Scale-sensitive Psi-dimensions: the Capacity Measures for Classifiers Taking Values in R^Q

TL;DR

This paper introduces new capacity measures called scale-sensitive Psi-dimensions for classifiers taking values in R^Q, providing improved risk bounds and advancing statistical learning theory.

Contribution

It generalizes VC dimension concepts to models with outputs in R^Q, offering a new risk guarantee for M-SVMs that surpasses previous bounds.

Findings

New capacity measure for R^Q-valued classifiers

Improved risk bounds for M-SVMs

Enhanced theoretical understanding of classifier capacity

Abstract

Bounds on the risk play a crucial role in statistical learning theory. They usually involve as capacity measure of the model studied the VC dimension or one of its extensions. In classification, such "VC dimensions" exist for models taking values in {0, 1}, {1,..., Q} and R. We introduce the generalizations appropriate for the missing case, the one of models with values in R^Q. This provides us with a new guaranteed risk for M-SVMs which appears superior to the existing one.