# Differentially Private Regression and Classification with Sparse Gaussian Processes

arXiv: https://arxiv.org/abs/1909.09147 · HTML: https://mlsanity.com/paper/1909.09147/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2019.

## Built on by (most cited first, 6 of 6)

- [Deep Learning with Label Differential Privacy](https://mlsanity.com/paper/2102.06062/) (2021)
- [DPlis: Boosting Utility of Differentially Private Deep Learning via Randomized Smoothing](https://mlsanity.com/paper/2103.01496/) (2021)
- [Gaussian Processes with Differential Privacy](https://mlsanity.com/paper/2106.00474/) (2021)
- [IRG: Modular Synthetic Relational Database Generation with Complex Relational Schemas](https://mlsanity.com/paper/2312.15187/) (2023)
- [RPWithPrior: Label Differential Privacy in Regression](https://mlsanity.com/paper/2601.22625/) (2026)
- [Differential Privacy of Gaussian Process Posterior Sampling](https://mlsanity.com/paper/2606.17995/) (2026)

## Abstract (arXiv)

A continuing challenge for machine learning is providing methods to perform computation on data while ensuring the data remains private. In this paper we build on the provable privacy guarantees of differential privacy which has been combined with Gaussian processes through the previously published cloaking method. In this paper we solve several shortcomings of this method, starting with the problem of predictions in regions with low data density. We experiment with the use of inducing points to provide a sparse approximation and show that these can provide robust differential privacy in outlier areas and at higher dimensions. We then look at classification, and modify the Laplace approximation approach to provide differentially private predictions. We then combine this with the sparse approximation and demonstrate the capability to perform classification in high dimensions. We finally explore the issue of hyperparameter selection and develop a method for their private selection. This paper and associated libraries provide a robust toolkit for combining differential privacy and GPs in a practical manner.