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arXiv · 1507.02971

Scalable MCMC for Large Data Problems using Data Subsampling and the Difference Estimator

Matias Quiroz·Mattias Villani·Robert Kohn
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Abstract

We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly efficient difference estimator from the survey sampling literature to estimate the log-likelihood accurately using only a small fraction of the data. Our algorithm improves on the $O(n)$ complexity of regular MCMC by operating over local data clusters instead of the full sample when computing the likelihood. The likelihood estimate is used in a Pseudo-marginal framework to sample from a perturbed posterior which is within $O(m^{-1/2})$ of the true posterior, where $m$ is the subsample size. The method is applied to a logistic regression model to predict firm bankruptcy for a large data set. We document a significant speed up in comparison to the standard MCMC on the full dataset.

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Matias Quiroz, Mattias Villani, Robert Kohn. 2015-07-10. Scalable MCMC for Large Data Problems using Data Subsampling and the Difference Estimator. https://arxiv.org/abs/1507.02971

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