# A Unified Framework for Human-Allied Learning of Probabilistic Circuits

arXiv: https://arxiv.org/abs/2405.02413 · HTML: https://mlsanity.com/paper/2405.02413/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 44 references that are in the map.
- First posted on arXiv 3 May 2024.

## Builds on (most cited first, 14 of 14)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [LayoutGAN: Generating Graphic Layouts with Wireframe Discriminators](https://mlsanity.com/paper/1901.06767/) (2019)
- [Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuits](https://mlsanity.com/paper/2004.06231/) (2020)
- [SetVAE: Learning Hierarchical Composition for Generative Modeling of Set-Structured Data](https://mlsanity.com/paper/2103.15619/) (2021)
- [Deep Set Prediction Networks](https://mlsanity.com/paper/1906.06565/) (2019)
- [Scaling Up Probabilistic Circuits by Latent Variable Distillation](https://mlsanity.com/paper/2210.04398/) (2022)
- [Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures](https://mlsanity.com/paper/1905.08550/) (2019)
- [Strudel: Learning Structured-Decomposable Probabilistic Circuits](https://mlsanity.com/paper/2007.09331/) (2020)
- [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)
- [VQ-Flows: Vector Quantized Local Normalizing Flows](https://mlsanity.com/paper/2203.11556/) (2022)
- [Probabilistic Circuits That Know What They Don't Know](https://mlsanity.com/paper/2302.06544/) (2023)
- [Exchangeability-Aware Sum-Product Networks](https://mlsanity.com/paper/2110.05165/) (2021)

## Built on by (most cited first, 5 of 5)

- [Tractable Representation Learning with Probabilistic Circuits](https://mlsanity.com/paper/2507.04385/) (2025)
- [Recursive Inference Machines for Neural Reasoning](https://mlsanity.com/paper/2603.05234/) (2026)
- [Geometry-Aware Probabilistic Circuits via Voronoi Tessellations](https://mlsanity.com/paper/2603.11946/) (2026)
- [A Neurosymbolic Approach for Explainable Early Diagnosis of Alzheimer's Disease](https://mlsanity.com/paper/2607.29530/) (2026)
- [A Compositional Theory of Curvature in Probabilistic Circuits](https://mlsanity.com/paper/2608.12869/) (2026)

## Abstract (arXiv)

Probabilistic Circuits (PCs) have emerged as an efficient framework for representing and learning complex probability distributions. Nevertheless, the existing body of research on PCs predominantly concentrates on data-driven parameter learning, often neglecting the potential of knowledge-intensive learning, a particular issue in data-scarce/knowledge-rich domains such as healthcare. To bridge this gap, we propose a novel unified framework that can systematically integrate diverse domain knowledge into the parameter learning process of PCs. Experiments on several benchmarks as well as real world datasets show that our proposed framework can both effectively and efficiently leverage domain knowledge to achieve superior performance compared to purely data-driven learning approaches.