Classification in asymmetric spaces via sample compression

TL;DR

This paper explores classification in asymmetric quasi-metric spaces, introducing a sample compression-based learning algorithm with proven statistical guarantees.

Contribution

It is the first to rigorously study classification in quasi-metric spaces and develop a sample compression-based algorithm with theoretical analysis.

Findings

Algorithm has favorable statistical properties

First rigorous study of classification in quasi-metric spaces

Sample compression approach effective in asymmetric settings

Abstract

We initiate the rigorous study of classification in quasi-metric spaces. These are point sets endowed with a distance function that is non-negative and also satisfies the triangle inequality, but is asymmetric. We develop and refine a learning algorithm for quasi-metrics based on sample compression and nearest neighbor, and prove that it has favorable statistical properties.