d64a340bcb633f536d56e51874281454-Reviews.html

Summary of the paper This paper is concerned with the support recovery problem in linear regression in the high dimensional setup, that is to say, recovery of the non null entries in the vector of regression parameters when the number of predictors p exceeds the sample size n. A simple greedy algorithm is proposed, particularly suitable in presence of high correlation between predictors: starting from an initial guess S of the true support, it swaps each of the variables in S to each of the variables in S c, one at a time, looking for improvement in the square loss. Such a procedure is called SWAP, and is typically used to enhance the performances of classical sparse recovery algorithms such as the LASSO, by using the latter as the initial guess for S. A theoretical analysis describing limitations and guarantees of SWAP are exposed in details: conditions for accurate support recovery and bounds for the number of iterations required are provided. It is shown that the required assumptions are milder than the usual irrepresentability condition. Comments The paper is clearly written and pleasant to read.