Efficient MCMC Sampling with Expensive-to-Compute and Irregular Likelihoods

2025-05-15

AI Summary

Bayesian inference under computationally expensive and nonsmooth likelihoods remains challenging due to prohibitive evaluation costs and the absence of reliable gradients. Method: This paper proposes a subset-driven delayed-acceptance MCMC framework comprising: (1) a data-driven surrogate model evaluated on random subsets—eliminating reliance on inaccurate gradients or Taylor approximations; (2) a computation-aware adaptive controller that jointly tunes proposal scale and subset size; and (3) a hierarchical delayed-acceptance mechanism that rapidly filters candidates via the coarse surrogate and rigorously validates them on the full dataset. Results: On real-world high-cost inference tasks—including disease modeling—the method significantly reduces sampling error under fixed computational budgets, balancing exploration efficiency and posterior accuracy. It outperforms state-of-the-art baselines (e.g., standard DA-MCMC, HINTS) in both convergence speed and estimation accuracy.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational overhead. We adapt the subset samplers for this setting where gradient information is not available or is unreliable. To achieve this, we introduce data-driven proxies in place of Taylor expansions and define a novel computation-cost aware adaptive controller. We undertake an extensive evaluation for a challenging disease modelling task and a configurable task with similar irregularity in the likelihood surface. We find our improved version of Hierarchical Importance with Nested Training Samples (HINTS), with adaptive proposals and a data-driven proxy, obtains the best sampling error in a fixed computational budget. We conclude that subset evaluations can provide cheap and naturally-tempered exploration, while a data-driven proxy can pre-screen proposals successfully in explored regions of the state space. These two elements combine through hierarchical delayed acceptance to achieve efficient, exact sampling.

Problem

• Efficient MCMC sampling with costly irregular likelihoods
• Adapting subset samplers without reliable gradient information
• Improving sampling accuracy using data-driven proxies and adaptive controllers

Innovation

• Subset samplers reduce computational overhead
• Data-driven proxies replace Taylor expansions
• Hierarchical delayed acceptance enables efficient sampling