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Informed Sub-Sampling MCMC: Approximate Bayesian Inference for Large Datasets

Author

Listed:
  • Florian Maire

    (School of Mathematics and Statistics, University College Dublin; Insight Centre for Data Analytics, University College Dublin)

  • Nial Friel

    (School of Mathematics and Statistics, University College Dublin; Insight Centre for Data Analytics, University College Dublin)

  • Pierre ALQUIER

    (CREST-ENSAE)

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 (ABC) 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 exible approach which, contrarily to existing scalable methodologies, preserves the simplicity of the Metropolis-Hastings algorithm. Even though exactness is lost, i.e the chain distribution approximates the target, 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.

Suggested Citation

  • Florian Maire & Nial Friel & Pierre ALQUIER, 2017. "Informed Sub-Sampling MCMC: Approximate Bayesian Inference for Large Datasets," Working Papers 2017-40, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2017-40
    as

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    References listed on IDEAS

    as
    1. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, November.
    2. Quiroz, Matias, 2015. "Speeding Up Mcmc By Delayed Acceptance And Data Subsampling," Working Paper Series 307, Sveriges Riksbank (Central Bank of Sweden).
    3. Nunes Matthew A & Balding David J, 2010. "On Optimal Selection of Summary Statistics for Approximate Bayesian Computation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-16, September.
    4. repec:dau:papers:123456789/5724 is not listed on IDEAS
    5. Matias Quiroz & Robert Kohn & Mattias Villani & Minh-Ngoc Tran, 2019. "Speeding Up MCMC by Efficient Data Subsampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 831-843, April.
    6. Paul Fearnhead & Dennis Prangle, 2012. "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 419-474, June.
    7. Arnak Dalalyan, 2017. "Further and stronger analogy between sampling and optimization: Langevin Monte Carlo and gradient descent," Working Papers 2017-21, Center for Research in Economics and Statistics.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Bayesian inference; Big-data; Approximate Bayesian Computation; noisy Markov chain Monte Carlo;
    All these keywords.

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