# Strudel: Learning Structured-Decomposable Probabilistic Circuits

arXiv: https://arxiv.org/abs/2007.09331 · HTML: https://mlsanity.com/paper/2007.09331/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2020.

## Built on by (most cited first, 24 of 24)

- [Tractable Regularization of Probabilistic Circuits](https://mlsanity.com/paper/2106.02264/) (2021)
- [Probabilistic Generating Circuits](https://mlsanity.com/paper/2102.09768/) (2021)
- [Lossless Compression with Probabilistic Circuits](https://mlsanity.com/paper/2111.11632/) (2021)
- [How to Turn Your Knowledge Graph Embeddings into Generative Models](https://mlsanity.com/paper/2305.15944/) (2023)
- [Continuous Mixtures of Tractable Probabilistic Models](https://mlsanity.com/paper/2209.10584/) (2022)
- [Understanding the Distillation Process from Deep Generative Models to Tractable Probabilistic Circuits](https://mlsanity.com/paper/2302.08086/) (2023)
- [Sparse Probabilistic Circuits via Pruning and Growing](https://mlsanity.com/paper/2211.12551/) (2022)
- [Building Expressive and Tractable Probabilistic Generative Models: A Review](https://mlsanity.com/paper/2402.00759/) (2024)
- [Solving Marginal MAP Exactly by Probabilistic Circuit Transformations](https://mlsanity.com/paper/2111.04833/) (2021)
- [Compositional Probabilistic and Causal Inference using Tractable Circuit Models](https://mlsanity.com/paper/2304.08278/) (2023)
- [Tractable Boolean and Arithmetic Circuits](https://mlsanity.com/paper/2202.02942/) (2022)
- [Characteristic Circuits](https://mlsanity.com/paper/2312.07790/) (2023)
- [A Compositional Atlas of Tractable Circuit Operations: From Simple Transformations to Complex Information-Theoretic Queries](https://mlsanity.com/paper/2102.06137/) (2021)
- [Bayesian Structure Scores for Probabilistic Circuits](https://mlsanity.com/paper/2302.12130/) (2023)
- [Restructuring Tractable Probabilistic Circuits](https://mlsanity.com/paper/2411.12256/) (2024)
- [Credibility-Aware Multi-Modal Fusion Using Probabilistic Circuits](https://mlsanity.com/paper/2403.03281/) (2024)
- [A Unified Framework for Human-Allied Learning of Probabilistic Circuits](https://mlsanity.com/paper/2405.02413/) (2024)
- [Tractable Computation of Expected Kernels](https://mlsanity.com/paper/2102.10562/) (2021)
- [Structural Learning of Probabilistic Sentential Decision Diagrams under Partial Closed-World Assumption](https://mlsanity.com/paper/2107.12130/) (2021)
- [Sum-Product-Attention Networks: Leveraging Self-Attention in Probabilistic Circuits](https://mlsanity.com/paper/2109.06587/) (2021)
- [Optimal Transport for Probabilistic Circuits](https://mlsanity.com/paper/2410.13061/) (2024)
- [A Sobering Look at Tabular Data Generation via Probabilistic Circuits](https://mlsanity.com/paper/2603.23016/) (2026)
- [SymCircuit: Bayesian Structure Inference for Tractable Probabilistic Circuits via Entropy-Regularized Reinforcement Learning](https://mlsanity.com/paper/2603.20392/) (2026)
- [The Expressivity Boundary of Probabilistic Circuits: A Comparison with Large Language Models](https://mlsanity.com/paper/2605.12940/) (2026)

## Abstract (arXiv)

Probabilistic circuits (PCs) represent a probability distribution as a computational graph. Enforcing structural properties on these graphs guarantees that several inference scenarios become tractable. Among these properties, structured decomposability is a particularly appealing one: it enables the efficient and exact computations of the probability of complex logical formulas, and can be used to reason about the expected output of certain predictive models under missing data. This paper proposes Strudel, a simple, fast and accurate learning algorithm for structured-decomposable PCs. Compared to prior work for learning structured-decomposable PCs, Strudel delivers more accurate single PC models in fewer iterations, and dramatically scales learning when building ensembles of PCs. It achieves this scalability by exploiting another structural property of PCs, called determinism, and by sharing the same computational graph across mixture components. We show these advantages on standard density estimation benchmarks and challenging inference scenarios.