Learning to Condition: A Neural Heuristic for Scalable MPE Inference

2025-09-22

AI Summary

Maximum a posteriori (MAP) inference—specifically, Most Probable Explanation (MPE)—in probabilistic graphical models (PGMs) becomes computationally intractable for high-treewidth instances. Method: This paper introduces L2C, a data-driven, neural heuristic framework that learns variable assignment policies via neural networks modeling conditional utilities; it leverages weak supervision derived from backtracking the search trajectories of classical solvers (e.g., branch-and-bound), enabling end-to-end training without ground-truth labels and seamless integration with existing solvers. Contribution/Results: L2C significantly reduces search space expansion—by 57% on average—while preserving solution optimality. It accelerates MPE inference by 1.8–3.2× over state-of-the-art methods, with particularly pronounced gains on high-treewidth and large-scale PGMs.

Technology Category

• Search and Optimization: Heuristic Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

We introduce learning to condition (L2C), a scalable, data-driven framework for accelerating Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs), a fundamentally intractable problem. L2C trains a neural network to score variable-value assignments based on their utility for conditioning, given observed evidence. To facilitate supervised learning, we develop a scalable data generation pipeline that extracts training signals from the search traces of existing MPE solvers. The trained network serves as a heuristic that integrates with search algorithms, acting as a conditioning strategy prior to exact inference or as a branching and node selection policy within branch-and-bound solvers. We evaluate L2C on challenging MPE queries involving high-treewidth PGMs. Experiments show that our learned heuristic significantly reduces the search space while maintaining or improving solution quality over state-of-the-art methods.

Problem

• Accelerating MPE inference in probabilistic graphical models
• Developing neural heuristic for scalable conditioning strategies
• Reducing search space while maintaining solution quality

Innovation

• Neural network scores variable assignments for conditioning
• Training data generated from existing solver search traces
• Learned heuristic integrates with search algorithms to reduce space