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Scalable Nonparametric Sampling from Multimodal Posteriors with the Posterior Bootstrap
Edwin Fong · Simon Lyddon · Christopher Holmes

Wed Jun 12 06:30 PM -- 09:00 PM (PDT) @ Pacific Ballroom #235

Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior modes. Furthermore, all models are misspecified, which brings into question the validity of the conventional Bayesian update. We present a scalable Bayesian nonparametric learning routine that enables posterior sampling through the optimization of suitably randomized objective functions. A Dirichlet process prior on the unknown data distribution accounts for model misspecification, and admits an embarrassingly parallel posterior bootstrap algorithm that generates independent and exact samples from the nonparametric posterior distribution. Our method is particularly adept at sampling from multimodal posterior distributions via a random restart mechanism, and we demonstrate this on Gaussian mixture model and sparse logistic regression examples.

Author Information

Edwin Fong (University of Oxford)
Simon Lyddon (University of Oxford)
Christopher Holmes (University of Oxford)

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