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PRIMO: Private Regression in Multiple Outcomes

arXiv 2303.04195 ↗First posted 7 Mar 2023cs.LG cs.CRcited by 0

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Abstract (arXiv)

We introduce a new private regression setting we call Private Regression in Multiple Outcomes (PRIMO), inspired by the common situation where a data analyst wants to perform a set of l regressions while preserving privacy, where the features X are shared across all l regressions, and each regression i ∈ [l] has a different vector of outcomes yi. Naively applying existing private linear regression techniques l times leads to a √l multiplicative increase in error over the standard linear regression setting. We apply a variety of techniques including sufficient statistics perturbation (SSP) and geometric projection-based methods to develop scalable algorithms that outperform this baseline across a range of parameter regimes. In particular, we obtain no dependence on l in the asymptotic error when l is sufficiently large. Empirically, on the task of genomic risk prediction with multiple phenotypes we find that even for values of l far smaller than the theory would predict, our projection-based method improves the accuracy relative to the variant that doesn't use the projection.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 23 of its 60 references that are in the map. First posted on arXiv 7 Mar 2023.

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23 of 60 references.

References · 23

  1. 2016Membership Inference Attacks against Machine Learning Modelscited by 2,221
  2. 2017Renyi Differential Privacycited by 643
  3. 2016Semi-supervised Knowledge Transfer for Deep Learning from Private Training Datacited by 347
  4. 2021Membership Inference Attacks on Machine Learning: A Surveycited by 306
  5. 2018Subsampled R'enyi Differential Privacy and Analytical Moments Accountantcited by 234
  6. 2020DP-CGAN: Differentially Private Synthetic Data and Label Generationcited by 118
  7. 2021Deep Learning with Label Differential Privacycited by 113
  8. 2015Algorithmic Stability for Adaptive Data Analysiscited by 88
  9. 2013Fingerprinting Codes and the Price of Approximate Differential Privacycited by 81
  10. 2015Generalization in Adaptive Data Analysis and Holdout Reusecited by 76
  11. 2019Graphical-model based estimation and inference for differential privacycited by 73
  12. 2018Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domaincited by 60
11 more
  1. 2021Differentially Private Query Release Through Adaptive Projectioncited by 50
  2. 2016On the Theory and Practice of Privacy-Preserving Bayesian Data Analysiscited by 34
  3. 2019The Power of Factorization Mechanisms in Local and Central Differential Privacycited by 30
  4. 2018Optimizing error of high-dimensional statistical queries under differential privacycited by 29
  5. 2021Label differential privacy via clusteringcited by 20
  6. 2013Efficient Algorithms for Privately Releasing Marginals via Convex Relaxationscited by 17
  7. 2014Private Multiplicative Weights Beyond Linear Queriescited by 17
  8. 2015Constructing Linear-Sized Spectral Sparsification in Almost-Linear Timecited by 17
  9. 2017Unbiased estimates for linear regression via volume samplingcited by 13
  10. 2022Differentially Private Regression with Unbounded Covariatescited by 10
  11. 2018How to Use Heuristics for Differential Privacycited by 6

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