Asymptotic Bayes Risk for Gaussian Mixture in a Semi-Supervised Setting

Semi-supervised learning (SSL) uses unlabeled data for training and has been shown to greatly improve performances when compared to a supervised approach on the labeled data available. This claim depends both on the amount of labeled data available and on the algorithm used. In this paper, we compute analytically the gap between the best fully-supervised approach on labeled data and the best semi-supervised approach using both labeled and unlabeled data, in a simple high-dimensional Gaussian mixture model. We quantify the best possible increase in performance obtained thanks to the unlabeled data, i.e. we compute the accuracy increase due to the information contained in the unlabeled data.