# Preserving Data Privacy in Learning Causal Structure with Fully Homomorphic Encryption

arXiv: https://arxiv.org/abs/2606.05129 · HTML: https://mlsanity.com/paper/2606.05129/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 3 Jun 2026.

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

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [EVA: An Encrypted Vector Arithmetic Language and Compiler for Efficient Homomorphic Computation](https://mlsanity.com/paper/1912.11951/) (2019)
- [Bayesian Network Constraint-Based Structure Learning Algorithms: Parallel and Optimised Implementations in the bnlearn R Package](https://mlsanity.com/paper/1406.7648/) (2014)
- [cuPC: CUDA-based Parallel PC Algorithm for Causal Structure Learning on GPU](https://mlsanity.com/paper/1812.08491/) (2018)
- [Efficient and Scalable Structure Learning for Bayesian Networks: Algorithms and Applications](https://mlsanity.com/paper/2012.03540/) (2020)
- [Towards Privacy-Aware Causal Structure Learning in Federated Setting](https://mlsanity.com/paper/2211.06919/) (2022)
- [PrivLava: Synthesizing Relational Data with Foreign Keys under Differential Privacy](https://mlsanity.com/paper/2304.04545/) (2023)
- [A review of homomorphic encryption and software tools for encrypted statistical machine learning](https://mlsanity.com/paper/1508.06574/) (2015)
- [A Branch-and-Bound Algorithm for MDL Learning Bayesian Networks](https://mlsanity.com/paper/1301.3897/) (2013)
- [Fast Parallel Bayesian Network Structure Learning](https://mlsanity.com/paper/2212.04259/) (2022)
- [Learning Bayesian Networks from Incomplete Data with Stochastic Search Algorithms](https://mlsanity.com/paper/1301.6726/) (2013)

## Abstract (arXiv)

Preserving data privacy is an important topic in structural data management and data mining. However, the issue of privacy leakage in distributed causal structure learning is a persistent challenge, especially in cases where data transmission and computation are required. In this paper, we propose a method based on fully homomorphic encryption (FHE) that performs calculations on ciphertexts, keeping data encrypted in transition and computation. Nevertheless, adopting FHE to causal structure learning is challenging due to the high computation cost and limited support on division as well as logarithm operations in FHE. To tackle this challenge, we propose a series of novel techniques including (i) circuit simplification for better efficiency, (ii) approximation of division and logarithm through Newton-Raphson Reciprocal and Taylor expansion, and (iii) a batching technique with SIMD-acceleration to enhance the whole learning process. Additionally, our method can be easily extended beyond FHE by demonstration of its portability to support differential privacy. Empirical results show that our method achieves high consistency and comparable causal structure with the plaintext version in the datasets tested. Last, our method is efficient and practical to complete learning causal structures in tens of minutes even under the privacy protection of FHE.