Approximately Bayes-Optimal Pseudo-Label Selection

Julian Martin Rodemann, Jann Goschenhofer, Emilio Dorigatti, Thomas Nagler, Thomas Augustin

Keywords: Bayesian Methods, Semi-Supervised Learning, Decision Theory, Self-Training, Approximate Inference, Robustness

TL;DR: We propose approximately Bayes-optimal selection of pseudo-samples in self-training to address the confirmation bias.

Abstract: Semi-supervised learning by self-training heavily relies on pseudo-label selection (PLS). This selection often depends on the initial model fit on labeled data. Early overfitting might thus be propagated to the final model by selecting instances with overconfident but erroneous predictions, often referred to as confirmation bias. This paper introduces BPLS, a Bayesian framework for PLS that aims to mitigate this issue. At its core lies a criterion for selecting instances to label: an analytical approximation of the posterior predictive of pseudo-samples. We derive this selection criterion by proving Bayes-optimality of the posterior predictive of pseudo-samples. We further overcome computational hurdles by approximating the criterion analytically. Its relation to the marginal likelihood allows us to come up with an approximation based on Laplace's method and the Gaussian integral. We empirically assess BPLS on simulated and real-world data. When faced with high-dimensional data prone to overfitting, BPLS outperforms traditional PLS methods.