Bayesian optimization for likelihood-free inference of simulator-based statistical models

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openAccess

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Volume Title

A2 Katsausartikkeli tieteellisessä aikakauslehdessä

Date

2016-08-01

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Mcode

Degree programme

Language

en

Pages

47
1-47

Series

Journal of Machine Learning Research, Volume 17

Abstract

Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We assume that only a finite number of parameters are of interest and allow the generative process to be very general; it may be a noisy nonlinear dynamical system with an unrestricted number of hidden variables. This weak assumption is useful for devising realistic models but it renders statistical inference very difficult. The main challenge is the intractability of the likelihood function. Several likelihood-free inference methods have been proposed which share the basic idea of identifying the parameters by finding values for which the discrepancy between simulated and observed data is small. A major obstacle to using these methods is their computational cost. The cost is largely due to the need to repeatedly simulate data sets and the lack of knowledge about how the parameters affect the discrepancy. We propose a strategy which combines probabilistic modeling of the discrepancy with optimization to facilitate likelihood-free inference. The strategy is implemented using Bayesian optimization and is shown to accelerate the inference through a reduction in the number of required simulations by several orders of magnitude.

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Keywords

Approximate Bayesian computation, Bayesian inference, Computational efficiency, Intractable likelihood, Latent variables

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Citation

Gutmann, M U & Corander, J 2016, ' Bayesian optimization for likelihood-free inference of simulator-based statistical models ', Journal of Machine Learning Research, vol. 17, pp. 1-47 . < http://jmlr.org/papers/v17/15-017.html >