Gaussian Processes to speed up MCMC with automatic exploratory-exploitation effect

2021/09/28 by Alessio Benavoli, Benavoli, Alessio, Jason Wyse +3
Computer Science · Decision Sciences · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Simulation Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2109.13891

openalex publication_date 2021/09/28 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

Abstract

We present a two-stage Metropolis-Hastings algorithm for sampling probabilistic models, whose log-likelihood is computationally expensive to evaluate, by using a surrogate Gaussian Process (GP) model. The key feature of the approach, and the difference w.r.t. previous works, is the ability to learn the target distribution from scratch (while sampling), and so without the need of pre-training the GP. This is fundamental for automatic and inference in Probabilistic Programming Languages In particular, we present an alternative first stage acceptance scheme by marginalising out the GP distributed function, which makes the acceptance ratio explicitly dependent on the variance of the GP. This approach is extended to Metropolis-Adjusted Langevin algorithm (MALA).

Citations

• Gaussian Processes for Big Data
• The pseudo-marginal approach for efficient Monte Carlo computations
• A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
• Monte Carlo sampling methods using Markov chains and their applications

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