Neural Information Processing Systems http://nips.cc/

Variational Bayesian Monte Carlo (VBMC) is a sample-efficient method for approximate Bayesian inference with computationally expensive likelihoods. While VBMC's local surrogate approach provides stable approximations, its conservative exploration strategy and limited evaluation budget can cause it to miss regions of complex posteriors. In this work, we introduce Stacking Variational Bayesian Monte Carlo (S-VBMC), a method that constructs global posterior approximations by merging independent VBMC runs through a principled and inexpensive post-processing step. Our approach leverages VBMC's mixture posterior representation and per-component evidence estimates, requiring no additional likelihood evaluations while being naturally parallelizable. We demonstrate S-VBMC's effectiveness on two synthetic problems designed to challenge VBMC's exploration capabilities and two real-world applications from computational neuroscience, showing substantial improvements in posterior approximation quality across all cases.

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.

Summary: The paper considers variational inference in the case where likelihood functions themselves are expensive to evaluate. It suggests approximating the ELBO using probabilistic numerics. A Gaussian process prior is placed on the log joint of the model. A novel acquisition function is proposed along with an approximation of the ELBO for a variational mixture distribution based on the GP posterior and simple Monte Carlo for the mixture entropy. Empirical comparison is performed against a variety of relevant baselines.

PyVBMC is a Python implementation of the Variational Bayesian Monte Carlo (VBMC) algorithm for posterior and model inference for black-box computational models (Acerbi, 2018, 2020). VBMC is an approximate inference method designed for efficient parameter estimation and model assessment when model evaluations are mildly-to-very expensive (e.g., a second or more) and/or noisy. Specifically, VBMC computes: - a flexible (non-Gaussian) approximate posterior distribution of the model parameters, from which statistics and posterior samples can be easily extracted; - an approximation of the model evidence or marginal likelihood, a metric used for Bayesian model selection. PyVBMC can be applied to any computational or statistical model with up to roughly 10-15 continuous parameters, with the only requirement that the user can provide a Python function that computes the target log likelihood of the model, or an approximation thereof (e.g., an estimate of the likelihood obtained via simulation or Monte Carlo methods). PyVBMC is particularly effective when the model takes more than about a second per evaluation, with dramatic speed-ups of 1-2 orders of magnitude when compared to traditional approximate inference methods. Extensive benchmarks on both artificial test problems and a large number of real models from the computational sciences, particularly computational and cognitive neuroscience, show that VBMC generally - and often vastly - outperforms alternative methods for sample-efficient Bayesian inference, and is applicable to both exact and simulator-based models (Acerbi, 2018, 2019, 2020). PyVBMC brings this state-of-the-art inference algorithm to Python, along with an easy-to-use Pythonic interface for running the algorithm and manipulating and visualizing its results.

PyBADS is a Python implementation of the Bayesian Adaptive Direct Search (BADS) algorithm for fast and robust black-box optimization (Acerbi and Ma 2017). BADS is an optimization algorithm designed to efficiently solve difficult optimization problems where the objective function is rough (non-convex, non-smooth), mildly expensive (e.g., the function evaluation requires more than 0.1 seconds), possibly noisy, and gradient information is unavailable. With BADS, these issues are well addressed, making it an excellent choice for fitting computational models using methods such as maximum-likelihood estimation. The algorithm scales efficiently to black-box functions with up to $D \approx 20$ continuous input parameters and supports bounds or no constraints. PyBADS comes along with an easy-to-use Pythonic interface for running the algorithm and inspecting its results. PyBADS only requires the user to provide a Python function for evaluating the target function, and optionally other constraints. Extensive benchmarks on both artificial test problems and large real model-fitting problems models drawn from cognitive, behavioral and computational neuroscience, show that BADS performs on par with or better than many other common and state-of-the-art optimizers (Acerbi and Ma 2017), making it a general model-fitting tool which provides fast and robust solutions.

We introduce Sparse Variational Bayesian Monte Carlo (SVBMC), a method for fast "post-process" Bayesian inference for models with black-box and potentially noisy likelihoods. SVBMC reuses all existing target density evaluations -- for example, from previous optimizations or partial Markov Chain Monte Carlo runs -- to build a sparse Gaussian process (GP) surrogate model of the log posterior density. Uncertain regions of the surrogate are then refined via active learning as needed. Our work builds on the Variational Bayesian Monte Carlo (VBMC) framework for sample-efficient inference, with several novel contributions. First, we make VBMC scalable to a large number of pre-existing evaluations via sparse GP regression, deriving novel Bayesian quadrature formulae and acquisition functions for active learning with sparse GPs. Second, we introduce noise shaping, a general technique to induce the sparse GP approximation to focus on high posterior density regions. Third, we prove theoretical results in support of the SVBMC refinement procedure. We validate our method on a variety of challenging synthetic scenarios and real-world applications. We find that SVBMC consistently builds good posterior approximations by post-processing of existing model evaluations from different sources, often requiring only a small number of additional density evaluations.

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.

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.

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.