An Orthogonal Matching Pursuit Variable Screening Algorithm for High-Dimensional Linear Regression Models

Algorithm 1

The OMP algorithm.

	Step 1 (Initialization). Set . Set the residual .
	Step 2 (Forward selection).
	(i) (2.1) Evaluation. In the th step , we are given . Then, for every , we compute
	,
	, is the projection onto the linear space spanned by the elements of and is the identity matrix.
	(ii) (2.2) Screening. We then find
	,
	and update accordingly.
	Step 3 (Solution path). Iterating Step 2 for times leads a total of nested candidate models. We then collect those models by a solution path with .