# Efficient Search-Based Weighted Model Integration

arXiv: https://arxiv.org/abs/1903.05334 · HTML: https://mlsanity.com/paper/1903.05334/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2019.

## Built on by (most cited first, 11 of 11)

- [SIMPLE: A Gradient Estimator for k-Subset Sampling](https://mlsanity.com/paper/2210.01941/) (2022)
- [A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfaction](https://mlsanity.com/paper/2503.19466/) (2025)
- [A Unified Approach to Count-Based Weakly-Supervised Learning](https://mlsanity.com/paper/2311.13718/) (2023)
- [Collapsed Inference for Bayesian Deep Learning](https://mlsanity.com/paper/2306.09686/) (2023)
- [Enhancing SMT-based Weighted Model Integration by Structure Awareness](https://mlsanity.com/paper/2302.06188/) (2023)
- [Declarative Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2302.10674/) (2023)
- [SMT-based Weighted Model Integration with Structure Awareness](https://mlsanity.com/paper/2206.13856/) (2022)
- [Context-Specific Likelihood Weighting](https://mlsanity.com/paper/2101.09791/) (2021)
- [Measure Theoretic Weighted Model Integration](https://mlsanity.com/paper/2103.13901/) (2021)
- [The Theory and Practice of MAP Inference over Non-Convex Constraints](https://mlsanity.com/paper/2602.08681/) (2026)
- [First-Order Context-Specific Likelihood Weighting in Hybrid Probabilistic Logic Programs](https://mlsanity.com/paper/2201.11165/) (2022)

## Abstract (arXiv)

Weighted model integration (WMI) extends Weighted model counting (WMC) to the integration of functions over mixed discrete-continuous domains. It has shown tremendous promise for solving inference problems in graphical models and probabilistic programming. Yet, state-of-the-art tools for WMI are limited in terms of performance and ignore the independence structure that is crucial to improving efficiency. To address this limitation, we propose an efficient model integration algorithm for theories with tree primal graphs. We exploit the sparse graph structure by using search to performing integration. Our algorithm greatly improves the computational efficiency on such problems and exploits context-specific independence between variables. Experimental results show dramatic speedups compared to existing WMI solvers on problems with tree-shaped dependencies.