The use of Bayesian models 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. 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 realworld datasets, and find that, in practice, the size of the coreset is independent of the original dataset size.
The work by REF introduces lower bounds on the total sensitivity of the logistic regression problem that is used in this paper.
Coresets for Scalable Bayesian Logistic Regression
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