From Cutting Planes Algorithms to Compression Schemes and Active Learning

TL;DR

This paper demonstrates that cutting-plane methods can be effectively adapted for machine learning tasks such as learning sparse classifiers, data compression, and active learning, offering a unified framework with practical benefits.

Contribution

It introduces a novel perspective on cutting-plane algorithms as versatile tools for machine learning, including active learning, beyond traditional optimization applications.

Findings

Cutting-plane methods enable learning sparse classifiers.

They provide effective data compression schemes.

They can be easily adapted into active learning algorithms.

Abstract

Cutting-plane methods are well-studied localization(and optimization) algorithms. We show that they provide a natural framework to perform machinelearning ---and not just to solve optimization problems posed by machinelearning--- in addition to their intended optimization use. In particular, theyallow one to learn sparse classifiers and provide good compression schemes.Moreover, we show that very little effort is required to turn them intoeffective active learning methods. This last property provides a generic way todesign a whole family of active learning algorithms from existing passivemethods. We present numerical simulations testifying of the relevance ofcutting-plane methods for passive and active learning tasks.