Efficient Amortized Bayesian Inference for Markov Random Fields via Gradient-Informed Grid Selection

2026-03-31

AI Summary

This work addresses the challenge of balancing computational cost and inference accuracy in Bayesian inference for intractable likelihood models such as Markov random fields. The authors propose an amortized MCMC framework that innovatively integrates gradient-guided grid point selection with Hermite interpolation to construct a smooth surrogate likelihood. Coupled with path sampling, this approach enables efficient approximate inference while preserving theoretical correctness and substantially reducing computational overhead. Experimental results demonstrate rapid convergence of inference accuracy with increasing grid density, and the method’s effectiveness and superiority are validated on both a satellite image hidden Potts model and an autologistic model of Arctic ice floes.

Technology Category

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

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Bayesian inference for models with intractable likelihoods, such as Markov random fields, poses a fundamental computational challenge due to the tradeoff between inferential accuracy and computational cost. Various MCMC methods have been developed to address this challenge. The exchange algorithm targets the exact posterior, but requires an expensive perfect sampling step at each iteration, which is often infeasible in practice. In contrast, path sampling approximates the Metropolis acceptance ratio using a precomputed grid of likelihood values, but may introduce bias when the grid is poorly chosen. We introduce a novel amortized MCMC framework that retains the theoretical validity of exact methods while substantially reducing the computational burden. The proposed approach employs a gradient-informed grid selection procedure and constructs a surrogate likelihood via Hermite interpolation, yielding a smooth approximation with low error. A simulation study characterizes the rate at which inferential accuracy improves as the number of grid points increases. We further demonstrate the practical performance of the method through applications to a hidden Potts model for satellite imagery and an autologistic model for Arctic ice floes.

Problem

• Bayesian inference
• Markov random fields
• intractable likelihoods
• computational cost
• inferential accuracy

Innovation

• amortized MCMC
• gradient-informed grid selection
• Hermite interpolation
• Markov random fields
• Bayesian inference