Easy Differentially Private Linear RegressionDownload PDF

Published: 01 Feb 2023, Last Modified: 17 Sept 2023ICLR 2023 posterReaders: Everyone
Keywords: differential privacy, linear regression
TL;DR: A practical algorithm for differentially private linear regression which does not require data bounds or parameter tuning but is competitive with methods that do.
Abstract: Linear regression is a fundamental tool for statistical analysis. This has motivated the development of linear regression methods that also satisfy differential privacy and thus guarantee that the learned model reveals little about any one data point used to construct it. However, existing differentially private solutions assume that the end user can easily specify good data bounds and hyperparameters. Both present significant practical obstacles. In this paper, we study an algorithm which uses the exponential mechanism to select a model with high Tukey depth from a collection of non-private regression models. Given $n$ samples of $d$-dimensional data used to train $m$ models, we construct an efficient analogue using an approximate Tukey depth that runs in time $O(d^2n + dm\log(m))$. We find that this algorithm obtains strong empirical performance in the data-rich setting with no data bounds or hyperparameter selection required.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Supplementary Material: zip
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics
Submission Guidelines: Yes
Please Choose The Closest Area That Your Submission Falls Into: Social Aspects of Machine Learning (eg, AI safety, fairness, privacy, interpretability, human-AI interaction, ethics)
Community Implementations: [![CatalyzeX](/images/catalyzex_icon.svg) 1 code implementation](https://www.catalyzex.com/paper/arxiv:2208.07353/code)
13 Replies