  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.
