← 研踪 PaperTrailarXiv:2610.39305 · v1
Learning to Bound: Monotonic, Calibrated Neural Upper Bounds for MPE Inference
首次提交 2026-10-29 11:51
版本更新 2026-10-29 11:51
雷达观测 2026-10-30 11:25
摘要
Probabilistic graphical models (PGMs) compactly encode structured joint distributions, but Most Probable Explanation (MPE), which finds the highest-probability assignment to unobserved variables, remains computationally intractable in large, densely structured models. Anytime systematic search, such as branch-and-bound (B&B), is a popular approach, but its efficiency depends on tight admissible upper bounds that are often prohibitively expensive to compute using classical methods like Mini-Bucket Elimination (MBE). We introduce Learning to Bound (L2B), a data-driven framework that amortizes bound computation cost by training a neural predictor. L2B targets two key properties required for effective search bounds: admissibility, which is achieved via statistical calibration techniques, and progressive tightening as evidence accumulates, which is enforced through structural architectural constraints that ensure monotonicity by construction. Across challenging benchmarks, L2B delivers tighter, monotonic bounds at orders-of-magnitude lower cost on every PGM family, and yields measurable improvements when integrated with branch-and-bound on high-treewidth instances.
作者备注：37 pages, 4 figures
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v1 · 2026-10-29 11:51 · 最新观测版本
Learning to Bound: Monotonic, Calibrated Neural Upper Bounds for MPE Inference
Probabilistic graphical models (PGMs) compactly encode structured joint distributions, but Most Probable Explanation (MPE), which finds the highest-probability assignment to unobserved variables, remains computationally intractable in large, densely structured models. Anytime systematic search, such as branch-and-bound (B&B), is a popular approach, but its efficiency depends on tight admissible upper bounds that are often prohibitively expensive to compute using classical methods like Mini-Bucket Elimination (MBE). We introduce Learning to Bound (L2B), a data-driven framework that amortizes bound computation cost by training a neural predictor. L2B targets two key properties required for effective search bounds: admissibility, which is achieved via statistical calibration techniques, and progressive tightening as evidence accumulates, which is enforced through structural architectural constraints that ensure monotonicity by construction. Across challenging benchmarks, L2B delivers tighter, monotonic bounds at orders-of-magnitude lower cost on every PGM family, and yields measurable improvements when integrated with branch-and-bound on high-treewidth instances.
查看此版本解读 →查看此版本原文 ↗