GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation

2014/01/13 by Edward Meeds, Max Welling, Meeds, Edward +1 · 5 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Biological sciences #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Quantitative Methods (q-bio.QM) #cs.LG #q-bio.QM #stat.ML

paper · pdf · doi:10.48550/arxiv.1401.2838

arxiv created 2014/01/13 · openalex publication_date 2014/01/13 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Scientists often express their understanding of the world through a computationally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challenging. The Approximate Bayesian Computation (ABC) framework is the standard statistical tool to handle these likelihood free problems, but they require a very large number of simulations. In this work we develop two new ABC sampling algorithms that significantly reduce the number of simulations necessary for posterior inference. Both algorithms use confidence estimates for the accept probability in the Metropolis Hastings step to adaptively choose the number of necessary simulations. Our GPS-ABC algorithm stores the information obtained from every simulation in a Gaussian process which acts as a surrogate function for the simulated statistics. Experiments on a challenging realistic biological problem illustrate the potential of these algorithms.

Citations

• A tutorial on approximate Bayesian computation
• The pseudo-marginal approach for efficient Monte Carlo computations
• Statistical inference for noisy nonlinear ecological dynamic systems
• A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
• Practical Bayesian Optimization of Machine Learning Algorithms
• Approximate Bayesian Computational methods

Cited by

• Sampling as Bandits: Evaluation-Efficient Design for Black-Box Densities
• Multilevel neural simulation-based inference
• Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Models
• Advances in Approximate Bayesian Inference for Models in Epidemiology
• Reducing Calls to the Simulator in Simulation Based Inference (SBI)

Related

• Accelerating ABC methods using Gaussian processes
• Approximate Bayesian Computation
• K2-ABC: Approximate Bayesian Computation with Kernel Embeddings
• Efficient learning in ABC algorithms
• Batch simulations and uncertainty quantification in Gaussian process surrogate approximate Bayesian computation