# Privacy-aware Gaussian Process Regression

arXiv: https://arxiv.org/abs/2305.16541 · HTML: https://mlsanity.com/paper/2305.16541/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 68 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 18 of 18)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [A general framework for Vecchia approximations of Gaussian processes](https://mlsanity.com/paper/1708.06302/) (2017)
- [Local Gaussian process approximation for large computer experiments](https://mlsanity.com/paper/1303.0383/) (2013)
- [Fast Matrix Square Roots with Applications to Gaussian Processes and Bayesian Optimization](https://mlsanity.com/paper/2006.11267/) (2020)
- [State Space Gaussian Processes with Non-Gaussian Likelihood](https://mlsanity.com/paper/1802.04846/) (2018)
- [Inferential Privacy Guarantees for Differentially Private Mechanisms](https://mlsanity.com/paper/1603.01508/) (2016)
- [Parallelizable sparse inverse formulation Gaussian processes (SpInGP)](https://mlsanity.com/paper/1610.08035/) (2016)
- [Kernel Packet: An Exact and Scalable Algorithm for Gaussian Process Regression with Mat'ern Correlations](https://mlsanity.com/paper/2203.03116/) (2022)
- [Fast prediction of deterministic functions using sparse grid experimental designs](https://mlsanity.com/paper/1402.6350/) (2014)
- [A Sparse Expansion For Deep Gaussian Processes](https://mlsanity.com/paper/2112.05888/) (2021)
- [Composition Properties of Inferential Privacy for Time-Series Data](https://mlsanity.com/paper/1707.02702/) (2017)
- [Gaussian Processes with Differential Privacy](https://mlsanity.com/paper/2106.00474/) (2021)
- [Ensuring Privacy with Constrained Additive Noise by Minimizing Fisher Information](https://mlsanity.com/paper/1808.09565/) (2018)
- [Kernel Interpolation with Sparse Grids](https://mlsanity.com/paper/2305.14451/) (2023)
- [Privacy and Utility Aware Data Sharing for Space Situational Awareness from Ensemble and Unscented Kalman Filtering Perspective](https://mlsanity.com/paper/1912.03775/) (2019)

## Abstract (arXiv)

We propose a novel theoretical and methodological framework for Gaussian process regression subject to privacy constraints. The proposed method can be used when a data owner is unwilling to share a high-fidelity supervised learning model built from their data with the public due to privacy concerns. The key idea of the proposed method is to add synthetic noise to the data until the predictive variance of the Gaussian process model reaches a prespecified privacy level. The optimal covariance matrix of the synthetic noise is formulated in terms of semi-definite programming. We also introduce the formulation of privacy-aware solutions under continuous privacy constraints using kernel-based approaches, and study their theoretical properties. The proposed method is illustrated by considering a model that tracks the trajectories of satellites and a real application on a census dataset.