Variational Bayesian Monte Carlo with Noisy Likelihoods
This work addresses the challenge of efficient Bayesian inference for researchers in fields like computational neuroscience dealing with noisy, simulation-based models, representing an incremental extension of the VBMC framework.
The authors tackled the problem of performing approximate Bayesian inference in models with noisy log-likelihood evaluations, such as simulation-based models, by extending Variational Bayesian Monte Carlo (VBMC) with new global acquisition functions like VIQR. In a challenging benchmark with real datasets from computational and cognitive neuroscience, VBMC+VIQR achieved state-of-the-art performance in recovering ground-truth posteriors and model evidence, vastly outperforming local acquisition functions and other surrogate-based methods while maintaining low algorithmic cost.
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.