Variational Bayesian Monte Carlo with Noisy Likelihoods

• URL: http://arxiv.org/abs/2006.08655v3
• Date: Mon, 19 Oct 2020 05:54:29 GMT
• Title: Variational Bayesian Monte Carlo with Noisy Likelihoods
• Authors: Luigi Acerbi
• Abstract summary: We introduce new global' acquisition functions, such as expected information gain (EIG) and variational interquantile range (VIQR) VBMC+VIQR achieves state-of-the-art performance in recovering the ground-truth posteriors and model evidence.
• Score: 11.4219428942199
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Variational Bayesian Monte Carlo (VBMC) is a recently introduced framework that uses Gaussian process surrogates to perform approximate Bayesian inference in models with black-box, non-cheap likelihoods. In this work, we extend VBMC to deal with noisy log-likelihood evaluations, such as those arising from simulation-based models. We introduce new `global' acquisition functions, such as expected information gain (EIG) and variational interquantile range (VIQR), which are robust to noise and can be efficiently evaluated within the VBMC setting. In a novel, challenging, noisy-inference benchmark comprising of a variety of models with real datasets from computational and cognitive neuroscience, VBMC+VIQR achieves state-of-the-art performance in recovering the ground-truth posteriors and model evidence. In particular, our method vastly outperforms `local' acquisition functions and other surrogate-based inference methods while keeping a small algorithmic cost. Our benchmark corroborates VBMC as a general-purpose technique for sample-efficient black-box Bayesian inference also with noisy models.

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