PRIMO: Private Regression in Multiple Outcomes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929676093489152 |
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| author | Neel, Seth |
| author_facet | Neel, Seth |
| contents | 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 $i \in [l]$ has a different vector of outcomes $y_i$. Naively applying existing private linear regression techniques $l$ times leads to a $\sqrt{l}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_04195 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | PRIMO: Private Regression in Multiple Outcomes Neel, Seth Machine Learning Cryptography and Security 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 $i \in [l]$ has a different vector of outcomes $y_i$. Naively applying existing private linear regression techniques $l$ times leads to a $\sqrt{l}$ 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. |
| title | PRIMO: Private Regression in Multiple Outcomes |
| topic | Machine Learning Cryptography and Security |
| url | https://arxiv.org/abs/2303.04195 |