Many probabilistic models of interest in scientific computing and machine
learning have expensive, black-box likelihoods that prevent the application of
standard techniques for Bayesian inference, such as MCMC, which would require
access to the gradient or a large number of likelihood evaluations. We
introduce here a novel sample-efficient inference framework, Variational
Bayesian Monte Carlo (VBMC). VBMC combines variational inference with
Gaussian-process based, active-sampling Bayesian quadrature, using the latter
to efficiently approximate the intractable integral in the variational
objective. Our method produces both a nonparametric approximation of the
posterior distribution and an approximate lower bound of the model evidence,
useful for model selection. We demonstrate VBMC both on several synthetic
likelihoods and on a neuronal model with data from real neurons. Across all
tested problems and dimensions (up to $D = 10$), VBMC performs consistently
well in reconstructing the posterior and the model evidence with a limited
budget of likelihood evaluations, unlike other methods that work only in very
low dimensions. Our framework shows great promise as a novel tool for posterior
and model inference with expensive, black-box likelihoods.

本文介绍了一种新型的高效样本推断框架，变分贝叶斯蒙特卡罗（VBMC），可用于难以处理的黑盒似然的后验分布和模型评估。该方法结合了变分推断和基于高斯过程的主动采样贝叶斯积分，并在合成和实际数据的测试中表现出很好的性能。