# Practical Privacy-Preserving Gaussian Process Regression via Secret Sharing

arXiv: https://arxiv.org/abs/2306.14498 · HTML: https://mlsanity.com/paper/2306.14498/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 49 references that are in the map.
- First posted on arXiv 26 Jun 2023.

## Builds on (most cited first, 15 of 15)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [iDLG: Improved Deep Leakage from Gradients](https://mlsanity.com/paper/2001.02610/) (2020)
- [CrypTen: Secure Multi-Party Computation Meets Machine Learning](https://mlsanity.com/paper/2109.00984/) (2021)
- [Federated Bayesian Optimization via Thompson Sampling](https://mlsanity.com/paper/2010.10154/) (2020)
- [No Free Lunch Theorem for Security and Utility in Federated Learning](https://mlsanity.com/paper/2203.05816/) (2022)
- [Differentially Private Federated Bayesian Optimization with Distributed Exploration](https://mlsanity.com/paper/2110.14153/) (2021)
- [ARIANN: Low-Interaction Privacy-Preserving Deep Learning via Function Secret Sharing](https://mlsanity.com/paper/2006.04593/) (2020)
- [Private Outsourced Bayesian Optimization](https://mlsanity.com/paper/2010.12799/) (2020)
- [Near-Optimal Active Learning of Multi-Output Gaussian Processes](https://mlsanity.com/paper/1511.06891/) (2015)
- [Federated Gaussian Process: Convergence, Automatic Personalization and Multi-fidelity Modeling](https://mlsanity.com/paper/2111.14008/) (2021)
- [Privacy-Preserving Gaussian Process Regression -- A Modular Approach to the Application of Homomorphic Encryption](https://mlsanity.com/paper/2001.10893/) (2020)
- [Fully Decentralized, Scalable Gaussian Processes for Multi-Agent Federated Learning](https://mlsanity.com/paper/2203.02865/) (2022)
- [Automated Insulin Delivery for Type 1 Diabetes Mellitus Patients using Gaussian Process-based Model Predictive Control](https://mlsanity.com/paper/2101.11887/) (2021)

## Built on by (most cited first, 2 of 2)

- [PrivLM-Bench: A Multi-level Privacy Evaluation Benchmark for Language Models](https://mlsanity.com/paper/2311.04044/) (2023)
- [SecFormer: Fast and Accurate Privacy-Preserving Inference for Transformer Models via SMPC](https://mlsanity.com/paper/2401.00793/) (2024)

## Abstract (arXiv)

Gaussian process regression (GPR) is a non-parametric model that has been used in many real-world applications that involve sensitive personal data (e.g., healthcare, finance, etc.) from multiple data owners. To fully and securely exploit the value of different data sources, this paper proposes a privacy-preserving GPR method based on secret sharing (SS), a secure multi-party computation (SMPC) technique. In contrast to existing studies that protect the data privacy of GPR via homomorphic encryption, differential privacy, or federated learning, our proposed method is more practical and can be used to preserve the data privacy of both the model inputs and outputs for various data-sharing scenarios (e.g., horizontally/vertically-partitioned data). However, it is non-trivial to directly apply SS on the conventional GPR algorithm, as it includes some operations whose accuracy and/or efficiency have not been well-enhanced in the current SMPC protocol. To address this issue, we derive a new SS-based exponentiation operation through the idea of 'confusion-correction' and construct an SS-based matrix inversion algorithm based on Cholesky decomposition. More importantly, we theoretically analyze the communication cost and the security of the proposed SS-based operations. Empirical results show that our proposed method can achieve reasonable accuracy and efficiency under the premise of preserving data privacy.