In the high-dimensional regression model a response variable is linearly
related to $p$ covariates, but the sample size $n$ is smaller than $p$. We
assume that only a small subset of covariates is `active' (i.e., the
corresponding coefficients are non-zero), and consider the model-selection
problem of identifying the active covariates. A popular approach is to estimate
the regression coefficients through the Lasso ($\ell_1$-regularized least
squares). This is known to correctly identify the active set only if the
irrelevant covariates are roughly orthogonal to the relevant ones, as
quantified through the so called `irrepresentability' condition. In this paper
we study the `Gauss-Lasso' selector, a simple two-stage method that first
solves the Lasso, and then performs ordinary least squares restricted to the
Lasso active set. We formulate `generalized irrepresentability condition'
(GIC), an assumption that is substantially weaker than irrepresentability. We
prove that, under GIC, the Gauss-Lasso correctly recovers the active set.

本文研究高维回归模型中只有少量自变量起作用的情况，提出了一种双阶段方法 Gauss-Lasso，并证明在满足广义不可表现性（GIC）条件时，Gauss-Lasso 可以正确识别自变量的作用。