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Speeding up MCMC by Efficient Data Subsampling

Author

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  • Kohn, Robert
  • Quiroz, Matias
  • Tran, Minh-Ngoc
  • Villani, Mattias

Abstract

We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for n observations is estimated from a random subset of m observations. We introduce a general and highly efficient unbiased estimator of the log-likelihood based on control variates obtained from clustering the data. The cost of computing the log-likelihood estimator is much smaller than that of the full log-likelihood used by standard MCMC. The likelihood estimate is bias-corrected and used in two correlated pseudo-marginal algorithms to sample from a perturbed posterior, for which we derive the asymptotic error with respect to n and m, respectively. A practical estimator of the error is proposed and we show that the error is negligible even for a very small m in our applications. We demonstrate that Subsampling MCMC is substantially more efficient than standard MCMC in terms of sampling efficiency for a given computational budget, and that it outperforms other subsampling methods for MCMC proposed in the literature.

Suggested Citation

  • Kohn, Robert & Quiroz, Matias & Tran, Minh-Ngoc & Villani, Mattias, 2016. "Speeding up MCMC by Efficient Data Subsampling," Working Papers 2123/16205, University of Sydney Business School, Discipline of Business Analytics.
  • Handle: RePEc:syb:wpbsba:2123/16205
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    References listed on IDEAS

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    1. Giordani, Paolo & Jacobson, Tor & Schedvin, Erik von & Villani, Mattias, 2014. "Taking the Twists into Account: Predicting Firm Bankruptcy Risk with Splines of Financial Ratios," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(04), pages 1071-1099, August.
    2. Tor Jacobson & Jesper Lindé & Kasper Roszbach, 2013. "Firm Default And Aggregate Fluctuations," Journal of the European Economic Association, European Economic Association, vol. 11(4), pages 945-972, August.
    3. Shujie Ma & Jeffrey S. Racine & Lijian Yang, 2015. "Spline Regression in the Presence of Categorical Predictors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 705-717, August.
    4. repec:dau:papers:123456789/5724 is not listed on IDEAS
    5. Pitt, Michael K. & Silva, Ralph dos Santos & Giordani, Paolo & Kohn, Robert, 2012. "On some properties of Markov chain Monte Carlo simulation methods based on the particle filter," Journal of Econometrics, Elsevier, vol. 171(2), pages 134-151.
    6. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    7. Quiroz, Matias & Villani, Mattias, 2013. "Dynamic mixture-of-experts models for longitudinal and discrete-time survival data," Working Paper Series 268, Sveriges Riksbank (Central Bank of Sweden).
    8. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
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    Citations

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    Cited by:

    1. 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.
    2. Quiroz, Matias & Villani, Mattias & Kohn, Robert, 2015. "Scalable Mcmc For Large Data Problems Using Data Subsampling And The Difference Estimator," Working Paper Series 306, Sveriges Riksbank (Central Bank of Sweden).

    More about this item

    Keywords

    Survey sampling; Big Data; Block pseudo-marginal; Estimated likelihood; Correlated pseudo-marginal; Bayesian inference;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods

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