# Compressive Statistical Learning with Random Feature Moments

## TL;DR

This paper introduces a framework called compressive statistical learning that compresses large datasets into low-dimensional sketches for efficient learning, demonstrated on PCA, clustering, and Gaussian mixture models.

## Contribution

It presents a novel approach to resource-efficient large-scale learning by using random feature moments to create informative data sketches.

## Key findings

- Sketch size controls generalization error
- Framework effectively applied to PCA, clustering, and Gaussian mixture models
- Reduces computational resources needed for large-scale learning

## 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 PCA, compressive clustering, and compressive Gaussian mixture Modeling with fixed known variance. The latter two are further developed in a companion paper.