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Informed sub-sampling MCMC: approximate Bayesian inference for large datasets

  • Florian Maire
  • Nial Friel
  • Pierre Alquier
Article

Abstract

This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an unknown fraction of fixed size of the available data that is randomly refreshed throughout the algorithm. Inspired by the Approximate Bayesian Computation literature, the subsampling process is guided by the fidelity to the observed data, as measured by summary statistics. The resulting algorithm, Informed Sub-Sampling MCMC, is a generic and flexible approach which, contrary to existing scalable methodologies, preserves the simplicity of the Metropolis–Hastings algorithm. Even though exactness is lost, i.e  the chain distribution approximates the posterior, we study and quantify theoretically this bias and show on a diverse set of examples that it yields excellent performances when the computational budget is limited. If available and cheap to compute, we show that setting the summary statistics as the maximum likelihood estimator is supported by theoretical arguments.

Keywords

Bayesian inference Big-data Approximate Bayesian Computation noisy Markov chain Monte Carlo 

Mathematics Subject Classification

Primary 65C40 65C60 Secondary 62F15 

Notes

Acknowledgements

The Insight Centre for Data Analytics is supported by Science Foundation Ireland under Grant Number SFI/12/RC/2289. Nial Friel’s research was also supported by an Science Foundation Ireland grant: 12/IP/1424. Pierre Alquier’s research was funded by Labex ECODEC (ANR - 11-LABEX-0047) and by the research programme New Challenges for New Data from LCL and GENES, hosted by the Fondation du Risque. We thank the Associate Editor and two anonymous Referees for their contribution to this work.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity College DublinDublinIreland
  2. 2.The Insight Centre of Data AnalyticsUniversity College DublinDublinIreland
  3. 3.CREST, ENSAEUniversité Paris SaclayParisFrance

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