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

2020/08/26 by Daniel Sanz-Alonso, Ruiyi Yang, Sanz-Alonso, Daniel +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Machine Learning and Data Classification #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2008.11809

openalex publication_date 2020/08/26 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28

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.

Citations

• Riemannian manifolds with uniformly bounded eigenfunctions
• A tutorial on spectral clustering
• Spectral Convergence of Graph Laplacian and Heat Kernel Reconstruction in L^∞ from Random Samples
• Spectral convergence of graph Laplacian and heat kernel reconstruction in L∞ from random samples

Cited by

• L²-posterior contraction rates for Gaussian process and random series priors in Bayesian nonparametric regression models

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