Title: Compressive Statistical Learning with Random Feature Moments,
Abstract: We describe a general framework --compressive statistical learning-- for
resource-efficient large-scale learning: the training collection is compressed
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. A near-minimizer of the risk is computed from the sketch through
the solution of a nonlinear least squares problem. We investigate sufficient
sketch sizes to control the generalization error of this procedure. The
framework is illustrated on compressive clustering, compressive Gaussian
mixture Modeling with fixed known variance, and compressive PCA.