Coresets for Scalable Bayesian Logistic Regression

TL;DR

This paper introduces an efficient method for creating small, weighted data subsets called coresets for Bayesian logistic regression, enabling scalable inference with theoretical guarantees and practical efficiency.

Contribution

It develops a novel coreset construction algorithm for Bayesian logistic regression with proven size and approximation guarantees, applicable in streaming and parallel contexts.

Findings

Coresets significantly reduce data size without losing accuracy.

Construction time is negligible compared to MCMC inference.

Coreset size is independent of original dataset size.

Abstract

The use of Bayesian methods in large-scale data settings is attractive because of the rich hierarchical models, uncertainty quantification, and prior specification they provide. Standard Bayesian inference algorithms are computationally expensive, however, making their direct application to large datasets difficult or infeasible. Recent work on scaling Bayesian inference has focused on modifying the underlying algorithms to, for example, use only a random data subsample at each iteration. We leverage the insight that data is often redundant to instead obtain a weighted subset of the data (called a coreset) that is much smaller than the original dataset. We can then use this small coreset in any number of existing posterior inference algorithms without modification. In this paper, we develop an efficient coreset construction algorithm for Bayesian logistic regression models. We provide theoretical guarantees on the size and approximation quality of the coreset -- both for fixed, known datasets, and in expectation for a wide class of data generative models. Crucially, the proposed approach also permits efficient construction of the coreset in both streaming and parallel settings, with minimal additional effort. We demonstrate the efficacy of our approach on a number of synthetic and real-world datasets, and find that, in practice, the size of the coreset is independent of the original dataset size. Furthermore, constructing the coreset takes a negligible amount of time compared to that required to run MCMC on it.