Fast post-process Bayesian inference with Variational Sparse Bayesian Quadrature

• URL: http://arxiv.org/abs/2303.05263v2
• Date: Tue, 18 Jun 2024 06:53:56 GMT
• Title: Fast post-process Bayesian inference with Variational Sparse Bayesian Quadrature
• Authors: Chengkun Li, Grégoire Clarté, Martin Jørgensen, Luigi Acerbi,
• Abstract summary: We propose the framework of post-process Bayesian inference as a means to obtain a quick posterior approximation from existing target density evaluations. Within this framework, we introduce Variational Sparse Bayesian Quadrature (VSBQ), a method for post-process approximate inference for models with black-box and potentially noisy likelihoods. We validate our method on challenging synthetic scenarios and real-world applications from computational neuroscience.
• Score: 13.36200518068162
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In applied Bayesian inference scenarios, users may have access to a large number of pre-existing model evaluations, for example from maximum-a-posteriori (MAP) optimization runs. However, traditional approximate inference techniques make little to no use of this available information. We propose the framework of post-process Bayesian inference as a means to obtain a quick posterior approximation from existing target density evaluations, with no further model calls. Within this framework, we introduce Variational Sparse Bayesian Quadrature (VSBQ), a method for post-process approximate inference for models with black-box and potentially noisy likelihoods. VSBQ reuses existing target density evaluations to build a sparse Gaussian process (GP) surrogate model of the log posterior density function. Subsequently, we leverage sparse-GP Bayesian quadrature combined with variational inference to achieve fast approximate posterior inference over the surrogate. We validate our method on challenging synthetic scenarios and real-world applications from computational neuroscience. The experiments show that VSBQ builds high-quality posterior approximations by post-processing existing optimization traces, with no further model evaluations.

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