# Probabilistic Circuits with Constraints via Convex Optimization

arXiv: https://arxiv.org/abs/2403.13125 · HTML: https://mlsanity.com/paper/2403.13125/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 36 references that are in the map.
- First posted on arXiv 19 Mar 2024.

## Builds on (most cited first, 13 of 13)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A survey on datasets for fairness-aware machine learning](https://mlsanity.com/paper/2110.00530/) (2021)
- [Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuits](https://mlsanity.com/paper/2004.06231/) (2020)
- [A Differential Approach to Inference in Bayesian Networks](https://mlsanity.com/paper/1301.3847/) (2013)
- [On the Latent Variable Interpretation in Sum-Product Networks](https://mlsanity.com/paper/1601.06180/) (2016)
- [Tractable Regularization of Probabilistic Circuits](https://mlsanity.com/paper/2106.02264/) (2021)
- [A Unified Approach for Learning the Parameters of Sum-Product Networks](https://mlsanity.com/paper/1601.00318/) (2016)
- [Bayesian Learning of Sum-Product Networks](https://mlsanity.com/paper/1905.10884/) (2019)
- [Joints in Random Forests](https://mlsanity.com/paper/2006.14937/) (2020)
- [Sum-product networks: A survey](https://mlsanity.com/paper/2004.01167/) (2020)
- [Automatic Bayesian Density Analysis](https://mlsanity.com/paper/1807.09306/) (2018)
- [Online Structure Learning for Sum-Product Networks with Gaussian Leaves](https://mlsanity.com/paper/1701.05265/) (2017)

## Built on by (most cited first, 1 of 1)

- [The Theory and Practice of MAP Inference over Non-Convex Constraints](https://mlsanity.com/paper/2602.08681/) (2026)

## Abstract (arXiv)

This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and marginal probabilities) while achieving state-of-the-art performance in some domains. The proposed approach takes both a PC and constraints as inputs, and outputs a new PC that satisfies the constraints. This is done efficiently via convex optimization without the need to retrain the entire model. Empirical evaluations indicate that the combination of constraints and PCs can have multiple use cases, including the improvement of model performance under scarce or incomplete data, as well as the enforcement of machine learning fairness measures into the model without compromising model fitness. We believe that these ideas will open possibilities for multiple other applications involving the combination of logics and deep probabilistic models.