Algorithmic Robustness for Learning via $(\epsilon, \gamma, \tau)$-Good Similarity Functions

TL;DR

This paper extends the theoretical understanding of $(, , )$-good similarity functions by providing a new generalization bound using the algorithmic robustness framework, enhancing guarantees for classifiers based on these functions.

Contribution

It introduces a novel generalization bound for classifiers using $(, , )$-good similarity functions through the algorithmic robustness approach, advancing the theoretical framework.

Findings

Provides a new generalization bound for similarity-based classifiers.

Connects similarity function properties with classifier performance.

Enhances theoretical guarantees for metric-based learning.

Abstract

The notion of metric plays a key role in machine learning problems such as classification, clustering or ranking. However, it is worth noting that there is a severe lack of theoretical guarantees that can be expected on the generalization capacity of the classifier associated to a given metric. The theoretical framework of $(\epsilon, \gamma, \tau)$-good similarity functions (Balcan et al., 2008) has been one of the first attempts to draw a link between the properties of a similarity function and those of a linear classifier making use of it. In this paper, we extend and complete this theory by providing a new generalization bound for the associated classifier based on the algorithmic robustness framework.