# N-Parties Private Structure and Parameter Learning for Sum-Product Networks

arXiv: https://arxiv.org/abs/2510.05946 · HTML: https://mlsanity.com/paper/2510.05946/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 33 references that are in the map.
- First posted on arXiv 7 Oct 2025.

## Builds on (most cited first, 9 of 9)

- [Bayesian Nonparametric Federated Learning of Neural Networks](https://mlsanity.com/paper/1905.12022/) (2019)
- [Federated Learning on Non-IID Data: A Survey](https://mlsanity.com/paper/2106.06843/) (2021)
- [CrypTen: Secure Multi-Party Computation Meets Machine Learning](https://mlsanity.com/paper/2109.00984/) (2021)
- [CryptGPU: Fast Privacy-Preserving Machine Learning on the GPU](https://mlsanity.com/paper/2104.10949/) (2021)
- [On the Latent Variable Interpretation in Sum-Product Networks](https://mlsanity.com/paper/1601.06180/) (2016)
- [Sum-product networks: A survey](https://mlsanity.com/paper/2004.01167/) (2020)
- [Neural Network Training With Homomorphic Encryption](https://mlsanity.com/paper/2012.13552/) (2020)
- [Comprehensive Performance Analysis of Homomorphic Cryptosystems for Practical Data Processing](https://mlsanity.com/paper/2202.02960/) (2022)
- [Certified Data Removal in Sum-Product Networks](https://mlsanity.com/paper/2210.01451/) (2022)

## Abstract (arXiv)

A sum-product network (SPN) is a graphical model that allows several types of probabilistic inference to be performed efficiently. In this paper, we propose a privacy-preserving protocol which tackles structure generation and parameter learning of SPNs. Additionally, we provide a protocol for private inference on SPNs, subsequent to training. To preserve the privacy of the participants, we derive our protocol based on secret sharing, which guarantees privacy in the honest-but-curious setting even when at most half of the parties cooperate to disclose the data. The protocol makes use of a forest of randomly generated SPNs, which is trained and weighted privately and can then be used for private inference on data points. Our experiments indicate that preserving the privacy of all participants does not decrease log-likelihood performance on both homogeneously and heterogeneously partitioned data. We furthermore show that our protocol's performance is comparable to current state-of-the-art SPN learners in homogeneously partitioned data settings. In terms of runtime and memory usage, we demonstrate that our implementation scales well when increasing the number of parties, comparing favorably to protocols for neural networks, when they are trained to reproduce the input-output behavior of SPNs.