Debiased LASSO under Poisson-Gauss Model

Pedro Abdalla; Gil Kur

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arXiv · 2402.16764

Debiased LASSO under Poisson-Gauss Model

Pedro Abdalla·Gil Kur

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Abstract

Quantifying uncertainty in high-dimensional sparse linear regression is a fundamental task in statistics that arises in various applications. One of the most successful methods for quantifying uncertainty is the debiased LASSO, which has a solid theoretical foundation but is restricted to settings where the noise is purely additive. Motivated by real-world applications, we study the so-called Poisson inverse problem with additive Gaussian noise and propose a debiased LASSO algorithm that only requires $n \gg s\log^2p$ samples, which is optimal up to a logarithmic factor.

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Pedro Abdalla, Gil Kur. 2024-02-26. Debiased LASSO under Poisson-Gauss Model. https://arxiv.org/abs/2402.16764

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