Papers › On the Computational Complexity of Private High-dimensional Model Selection

On the Computational Complexity of Private High-dimensional Model Selection

11 Oct 2023arXiv:2310.07852archive 2025-07-28

Saptarshi Roy, Zehua Wang, Ambuj Tewari

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.

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