Statistical learning guarantees for compressive clustering and compressive mixture modeling

Abstract

We provide statistical learning guarantees for two unsupervised learning tasks in the context of $compressive$ $statistical$ $learning$, a general framework for resource-efficient large-scale learning that we introduced in a companion paper. The principle of compressive statistical learning is to compress a training collection, in one pass, into a low-dimensional $sketch$ (a vector of random empirical generalized moments) that captures the information relevant to the considered learning task. We explicitly describe and analyze random feature functions which empirical averages preserve the needed information for $compressive$ $clustering$ and $compressive$ $Gaussian$ $mixture$ $modeling$ with fixed known variance, and establish sufficient sketch sizes given the problem dimensions.