Unlabeled Data Help in Graph-Based Semi-Supervised Learning: A Bayesian Nonparametrics Perspective

TL;DR

This paper provides a Bayesian analysis of graph-based semi-supervised learning, showing that with enough unlabeled data, the posterior concentrates near the true function at near-optimal rates for both regression and classification.

Contribution

It introduces a Bayesian framework that explains how unlabeled data improve semi-supervised learning, achieving near-minimax optimal convergence rates.

Findings

Posterior contracts around the true function at near-minimax rates.

The theory applies to both regression and classification tasks.

Unlabeled data significantly enhance learning performance under the Bayesian approach.

Abstract

In this paper we analyze the graph-based approach to semi-supervised learning under a manifold assumption. We adopt a Bayesian perspective and demonstrate that, for a suitable choice of prior constructed with sufficiently many unlabeled data, the posterior contracts around the truth at a rate that is minimax optimal up to a logarithmic factor. Our theory covers both regression and classification.