Density-sensitive semisupervised inference

Abstract

Semisupervised methods are techniques for using labeled data $(X_1,Y_1),\dots ,(X_n,Y_n)$ together with unlabeled data $X_{n+1},\dots ,X_N$ to make predictions. These methods invoke some assumptions that link the marginal distribution $P_X$ of X to the regression function f(x). For example, it is common to assume that f is very smooth over high density regions of $P_X$. Many of the methods are ad-hoc and have been shown to work in specific examples but are lacking a theoretical foundation. We provide a minimax framework for analyzing semisupervised methods. In particular, we study methods based on metrics that are sensitive to the distribution $P_X$. Our model includes a parameter $\alpha$ that controls the strength of the semisupervised assumption. We then use the data to adapt to $\alpha$.

Published in at http://dx.doi.org/10.1214/13-AOS1092 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• k-NN Regression Adapts to Local Intrinsic Dimension
• The Use of Unlabeled Data in Predictive Modeling
• Semi-supervised Learning with Density Based Distances