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.

翻译：在高维稀疏线性回归中量化不确定性是统计学中的一项基本任务，出现在多种应用中。最成功的不确定性量化方法之一是去偏LASSO，该方法具有坚实的理论基础，但仅适用于噪声为纯加性噪声的场景。受实际应用启发，我们研究了带有加性高斯噪声的所谓泊松逆问题，并提出了一种去偏LASSO算法，该算法仅需$n \gg s\log^2p$个样本，这在对数因子意义下是最优的。