DENSITY-SENSITIVE SEMISUPERVISED INFERENCE

Semisupervised methods are techniques for using labeled data (X 1 , Y 1 ),..., (X n , Y n ) together with unlabeled data X n+1 ,...,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 . that controls the strength of the semisupervised assumption. We then use the data to adapt to ..