# Learning to Solve the Constrained Most Probable Explanation Task in Probabilistic Graphical Models

arXiv: https://arxiv.org/abs/2404.11606 · HTML: https://mlsanity.com/paper/2404.11606/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 48 references that are in the map.
- First posted on arXiv 17 Apr 2024.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [On The Reasons Behind Decisions](https://mlsanity.com/paper/2002.09284/) (2020)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [Neural Enhanced Belief Propagation on Factor Graphs](https://mlsanity.com/paper/2003.01998/) (2020)
- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [Belief Propagation Neural Networks](https://mlsanity.com/paper/2007.00295/) (2020)
- [Learning Hard Optimization Problems: A Data Generation Perspective](https://mlsanity.com/paper/2106.02601/) (2021)
- [Factor Graph Neural Networks](https://mlsanity.com/paper/2308.00887/) (2023)

## Built on by (most cited first, 3 of 3)

- [Addressing Class Imbalance with Probabilistic Graphical Models and Variational Inference](https://mlsanity.com/paper/2504.05758/) (2025)
- [ReMAP: Lossless Residual Neural Lifting for Scalable MAP Inference in Arbitrary-Order Markov Random Fields](https://mlsanity.com/paper/2411.18954/) (2024)
- [Learning to Guide Local Search for MPE Inference in Probabilistic Graphical Models](https://mlsanity.com/paper/2602.01475/) (2026)

## Abstract (arXiv)

We propose a self-supervised learning approach for solving the following constrained optimization task in log-linear models or Markov networks. Let f and g be two log-linear models defined over the sets X and Y of random variables respectively. Given an assignment x to all variables in X (evidence) and a real number q, the constrained most-probable explanation (CMPE) task seeks to find an assignment y to all variables in Y such that f(x, y) is maximized and g(x, y)≤ q. In our proposed self-supervised approach, given assignments x to X (data), we train a deep neural network that learns to output near-optimal solutions to the CMPE problem without requiring access to any pre-computed solutions. The key idea in our approach is to use first principles and approximate inference methods for CMPE to derive novel loss functions that seek to push infeasible solutions towards feasible ones and feasible solutions towards optimal ones. We analyze the properties of our proposed method and experimentally demonstrate its efficacy on several benchmark problems.