On the Computational Complexity of Private High-dimensional Model Selection
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914995968671744 |
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| author | Roy, Saptarshi Wang, Zehua Tewari, Ambuj |
| author_facet | Roy, Saptarshi Wang, Zehua Tewari, Ambuj |
| contents | We consider the problem of model selection in a high-dimensional sparse linear regression model under privacy constraints. We propose a differentially private (DP) best subset selection method with strong statistical utility properties by adopting the well-known exponential mechanism for selecting the best model. To achieve computational expediency, we propose an efficient Metropolis-Hastings algorithm and under certain regularity conditions, we establish that it enjoys polynomial mixing time to its stationary distribution. As a result, we also establish both approximate differential privacy and statistical utility for the estimates of the mixed Metropolis-Hastings chain. Finally, we perform some illustrative experiments on simulated data showing that our algorithm can quickly identify active features under reasonable privacy budget constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07852 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Computational Complexity of Private High-dimensional Model Selection Roy, Saptarshi Wang, Zehua Tewari, Ambuj Machine Learning Computation Methodology We consider the problem of model selection in a high-dimensional sparse linear regression model under privacy constraints. We propose a differentially private (DP) best subset selection method with strong statistical utility properties by adopting the well-known exponential mechanism for selecting the best model. To achieve computational expediency, we propose an efficient Metropolis-Hastings algorithm and under certain regularity conditions, we establish that it enjoys polynomial mixing time to its stationary distribution. As a result, we also establish both approximate differential privacy and statistical utility for the estimates of the mixed Metropolis-Hastings chain. Finally, we perform some illustrative experiments on simulated data showing that our algorithm can quickly identify active features under reasonable privacy budget constraints. |
| title | On the Computational Complexity of Private High-dimensional Model Selection |
| topic | Machine Learning Computation Methodology |
| url | https://arxiv.org/abs/2310.07852 |