Smoothed Analysis of Learning from Positive Samples

Binary classification from positive-only samples is a variant of PAC learning where the learner receives i.i.d. positively labeled samples and aims to learn a classifier that, with high probability, achieves low classification error. Previous work by Natarajan in STOC 1987 and Shvaytser in 1990 characterized learnability in this setting and revealed a largely negative picture: almost no interesting classes, including two-dimensional halfspaces, are learnablefrom positive-only examples. This poses significant challenges for the plethora of applications of positive-only learning from bioinformatics to ecology, where practitioners rely on heuristics for learning.