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.

本文提出了一种基于 Bayesian 方法的核心子集构造算法，可有效加速后验推断算法，适用于大规模数据集。该方法具有明显的理论保证和实际效果。