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Debiased LASSO under Poisson-Gauss Model (2402.16764v1)
Published 26 Feb 2024 in math.ST, cs.IT, eess.SP, math.IT, and stat.TH
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 $n \gg s\log2p$ samples, which is optimal up to a logarithmic factor.
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