Variational Bayesian Monte Carlo with Noisy Likelihoods

TL;DR

This paper extends Variational Bayesian Monte Carlo (VBMC) to handle noisy likelihoods, introducing robust acquisition functions that improve inference accuracy and efficiency in complex, noisy models from neuroscience.

Contribution

The authors develop noise-robust acquisition functions for VBMC, enabling effective Bayesian inference in noisy, black-box models with real-world data.

Findings

VBMC+VIQR outperforms existing methods in recovering true posteriors.

The new approach is computationally efficient and robust to noise.

Benchmark results show state-of-the-art performance in neuroscience models.

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.