Unlabeled Data Help in Graph-Based Semi-Supervised Learning: A Bayesian Nonparametrics Perspective
This provides theoretical guarantees for semi-supervised learning methods, which is incremental but important for practitioners in machine learning.
The paper tackles the problem of analyzing graph-based semi-supervised learning under a manifold assumption by adopting a Bayesian perspective, showing that with a suitable prior and sufficient unlabeled data, the posterior contracts around the truth at a minimax optimal rate up to a logarithmic factor for regression and classification.
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.