Compressive statistical learning with random feature moments

We describe a general framework --compressive statistical learning-- for resource-efficient large-scale learning: the training collection is compressed in one pass into low-dimensional sketch (a vector of random empirical generalized moments) that captures information relevant to considered learning task. A near-minimizer risk computed from through solution nonlinear least squares problem. investigate sufficient sizes control generalization error this procedure. The illustrated on compressive PCA, clustering, and Gaussian mixture Modeling with fixed known variance. latter two are further developed companion paper.