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On the consistency of graph-based Bayesian semi-supervised learning and the scalability of sampling algorithms

Nicolas Garcia Trillos, Zachary Kaplan, Thabo Samakhoana, Daniel Sanz-Alonso; 21(28):1−47, 2020.

Abstract

This paper considers a Bayesian approach to graph-based semi-supervised learning. We show that if the graph parameters are suitably scaled, the graph-posteriors converge to a continuum limit as the size of the unlabeled data set grows. This consistency result has profound algorithmic implications: we prove that when consistency holds, carefully designed Markov chain Monte Carlo algorithms have a uniform spectral gap, independent of the number of unlabeled inputs. Numerical experiments illustrate and complement the theory.

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