Learning to Condition: A Neural Heuristic for Scalable MPE Inference

TL;DR

This work tackles the NP-hard challenge of Most Probable Explanation inference in probabilistic graphical models by learning a conditioning strategy. It introduces Learning to Condition (L2C), a dual-head neural architecture that assigns optimality and simplification scores to variable-value assignments, trained via a scalable data-generation pipeline that uses solver traces and oracle solutions. The method yields improvements in both greedy conditioning and NN-guided branch-and-bound, significantly reducing search space while maintaining or improving solution quality on high-treewidth PGMs. By enabling instance-specific conditioning decisions and integration with exact and approximate solvers, L2C offers a practical pathway to scalable and accurate MPE inference in complex graphical models.

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.

Figures (49)

• Figure 1: Attention-based architecture for scoring variable-value pairs by their utility in simplifying MPE inference while preserving optimality.
• Figure 2: Neural vs. baseline methods for greedy conditioning (SCIP oracle). (a) Win counts; (b) Log-likelihood gaps. Color: Darker green = stronger, darker red = weaker performance. Grey: Timeouts (30s).
• Figure 3: Greedy conditioning methods (AOBB oracle): Average solution gap (x-axis) versus % node reduction (y-axis). Each subfigure denotes a fixed decision count.
• Figure 4: Heuristic comparison across datasets (rows) and time limits (columns); darker green/red indicates better/worse L2C-Rank performance.
• Figure 5: Average percentage gap on the BN 12 network for greedy conditioning using our methods, L2C-Opt and L2C-Rank, and baseline approaches across varying time budgets and numbers of decisions. More negative values indicate better performance.