Training Gaussian Mixture Models at Scale via Coresets

TL;DR

This paper introduces a method to create small, weighted subsets called coresets for Gaussian mixture models, enabling efficient training on large datasets without sacrificing accuracy.

Contribution

The paper presents the first polynomial-sized coresets for Gaussian mixtures, applicable in distributed and streaming contexts, based on novel geometric and combinatorial techniques.

Findings

Coresets significantly reduce training time.

Coresets maintain high approximation accuracy.

Method is applicable to real-world datasets.

Abstract

How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also provide a good fit for the original data set. We show that, perhaps surprisingly, Gaussian mixtures admit coresets of size polynomial in dimension and the number of mixture components, while being independent of the data set size. Hence, one can harness computationally intensive algorithms to compute a good approximation on a significantly smaller data set. More importantly, such coresets can be efficiently constructed both in distributed and streaming settings and do not impose restrictions on the data generating process. Our results rely on a novel reduction of statistical estimation to problems in computational geometry and new combinatorial complexity results for mixtures of Gaussians. Empirical evaluation on several real-world datasets suggests that our coreset-based approach enables significant reduction in training-time with negligible approximation error.