# Scaling Probabilistic Circuits via Data Partitioning

arXiv: https://arxiv.org/abs/2503.08141 · HTML: https://mlsanity.com/paper/2503.08141/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 16 of 16)

- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Split learning for health: Distributed deep learning without sharing raw patient data](https://mlsanity.com/paper/1812.00564/) (2018)
- [A Survey on Federated Learning Systems: Vision, Hype and Reality for Data Privacy and Protection](https://mlsanity.com/paper/1907.09693/) (2019)
- [SecureBoost: A Lossless Federated Learning Framework](https://mlsanity.com/paper/1901.08755/) (2019)
- [Mime: Mimicking Centralized Stochastic Algorithms in Federated Learning](https://mlsanity.com/paper/2008.03606/) (2020)
- [Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuits](https://mlsanity.com/paper/2004.06231/) (2020)
- [Privacy Preserving Vertical Federated Learning for Tree-based Models](https://mlsanity.com/paper/2008.06170/) (2020)
- [VAFL: a Method of Vertical Asynchronous Federated Learning](https://mlsanity.com/paper/2007.06081/) (2020)
- [SplitNN-driven Vertical Partitioning](https://mlsanity.com/paper/2008.04137/) (2020)
- [Scaling Up Probabilistic Circuits by Latent Variable Distillation](https://mlsanity.com/paper/2210.04398/) (2022)
- [A Communication Efficient Collaborative Learning Framework for Distributed Features](https://mlsanity.com/paper/1912.11187/) (2019)
- [Sum-product networks: A survey](https://mlsanity.com/paper/2004.01167/) (2020)
- [Hybrid Federated Learning: Algorithms and Implementation](https://mlsanity.com/paper/2012.12420/) (2020)
- [Effective and Efficient Federated Tree Learning on Hybrid Data](https://mlsanity.com/paper/2310.11865/) (2023)
- [VHT: Vertical Hoeffding Tree](https://mlsanity.com/paper/1607.08325/) (2016)

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

- [ExplainFuzz: Explainable and Constraint-Conditioned Test Generation with Probabilistic Circuits](https://mlsanity.com/paper/2604.06559/) (2026)

## Abstract (arXiv)

Probabilistic circuits (PCs) enable us to learn joint distributions over a set of random variables and to perform various probabilistic queries in a tractable fashion. Though the tractability property allows PCs to scale beyond non-tractable models such as Bayesian Networks, scaling training and inference of PCs to larger, real-world datasets remains challenging. To remedy the situation, we show how PCs can be learned across multiple machines by recursively partitioning a distributed dataset, thereby unveiling a deep connection between PCs and federated learning (FL). This leads to federated circuits (FCs) -- a novel and flexible federated learning (FL) framework that (1) allows one to scale PCs on distributed learning environments (2) train PCs faster and (3) unifies for the first time horizontal, vertical, and hybrid FL in one framework by re-framing FL as a density estimation problem over distributed datasets. We demonstrate FC's capability to scale PCs on various large-scale datasets. Also, we show FC's versatility in handling horizontal, vertical, and hybrid FL within a unified framework on multiple classification tasks.