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We propose a novel sampling framework for inference in probabilistic models:an active learning approach that converges more quickly (in wall-clock time)than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge inprobabilistic inference is numerical integration, to average over ensembles ofmodels or unknown (hyper-)parameters (for example to compute the marginallikelihood or a partition function). MCMC has provided approaches to numericalintegration that deliver state-of-the-art inference, but can suffer from sampleinefficiency and poor convergence diagnostics. Bayesian quadrature techniquesoffer a model-based solution to such problems, but their uptake has beenhindered by prohibitive computation costs. We introduce a warped model forprobabilistic integrands (likelihoods) that are known to be non-negative,permitting a cheap active learning scheme to optimally select sample locations.Our algorithm is demonstrated to offer faster convergence (in seconds) relativeto simple Monte Carlo and annealed importance sampling on both synthetic andreal-world examples.

Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature