# Gaussian Processes with Differential Privacy

arXiv: https://arxiv.org/abs/2106.00474 · HTML: https://mlsanity.com/paper/2106.00474/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 27 references that are in the map.
- First posted on arXiv 1 Jun 2021.

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

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Private Selection from Private Candidates](https://mlsanity.com/paper/1811.07971/) (2018)
- [CoinPress: Practical Private Mean and Covariance Estimation](https://mlsanity.com/paper/2006.06618/) (2020)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain](https://mlsanity.com/paper/1803.02596/) (2018)
- [Dirichlet-based Gaussian Processes for Large-scale Calibrated Classification](https://mlsanity.com/paper/1805.10915/) (2018)
- [Differentially Private Bayesian Linear Regression](https://mlsanity.com/paper/1910.13153/) (2019)
- [Differentially Private Markov Chain Monte Carlo](https://mlsanity.com/paper/1901.10275/) (2019)
- [Differentially Private Variational Inference for Non-conjugate Models](https://mlsanity.com/paper/1610.08749/) (2016)
- [Differentially Private Bayesian Inference for Generalized Linear Models](https://mlsanity.com/paper/2011.00467/) (2020)
- [Differentially Private Regression and Classification with Sparse Gaussian Processes](https://mlsanity.com/paper/1909.09147/) (2019)

## Built on by (most cited first, 3 of 3)

- [A Secure Federated Data-Driven Evolutionary Multi-objective Optimization Algorithm](https://mlsanity.com/paper/2210.08295/) (2022)
- [Privacy-aware Gaussian Process Regression](https://mlsanity.com/paper/2305.16541/) (2023)
- [Differential Privacy of Gaussian Process Posterior Sampling](https://mlsanity.com/paper/2606.17995/) (2026)

## Abstract (arXiv)

Gaussian processes (GPs) are non-parametric Bayesian models that are widely used for diverse prediction tasks. Previous work in adding strong privacy protection to GPs via differential privacy (DP) has been limited to protecting only the privacy of the prediction targets (model outputs) but not inputs. We break this limitation by introducing GPs with DP protection for both model inputs and outputs. We achieve this by using sparse GP methodology and publishing a private variational approximation on known inducing points. The approximation covariance is adjusted to approximately account for the added uncertainty from DP noise. The approximation can be used to compute arbitrary predictions using standard sparse GP techniques. We propose a method for hyperparameter learning using a private selection protocol applied to validation set log-likelihood. Our experiments demonstrate that given sufficient amount of data, the method can produce accurate models under strong privacy protection.