Generalization error bounds in semi-supervised classification under the cluster assumption

TL;DR

This paper derives generalization error bounds for semi-supervised classification under the cluster assumption, leveraging density level set estimation to improve convergence rates with both labeled and unlabeled data.

Contribution

It provides a formal mathematical formulation of the cluster assumption and introduces a method that exploits it for faster convergence in semi-supervised learning.

Findings

Achieves fast convergence rates using unlabeled data

Formalizes the cluster assumption mathematically

Demonstrates benefits of density level set estimation

Abstract

We consider semi-supervised classification when part of the available data is unlabeled. These unlabeled data can be useful for the classification problem when we make an assumption relating the behavior of the regression function to that of the marginal distribution. Seeger (2000) proposed the well-known "cluster assumption" as a reasonable one. We propose a mathematical formulation of this assumption and a method based on density level sets estimation that takes advantage of it to achieve fast rates of convergence both in the number of unlabeled examples and the number of labeled examples.