create.solve_equi: Optimization for equi-correlated fixed-X and Gaussian...

In knockoff: The Knockoff Filter for Controlled Variable Selection

Optimization for equi-correlated fixed-X and Gaussian knockoffs

Description

This function solves a very simple optimization problem needed to create fixed-X and Gaussian SDP knockoffs on the full the covariance matrix. This may be significantly less powerful than create.solve_sdp.

Usage

create.solve_equi(Sigma)

Arguments

Sigma

positive-definite p-by-p covariance matrix.

Details

Computes the closed-form solution to the semidefinite programming problem:

\mathrm{maximize} \; s \quad \mathrm{subject} \; \mathrm{to:} \; 0 ≤q s ≤q 1, \; 2Σ - sI ≥q 0

used to generate equi-correlated knockoffs.

The closed form-solution to this problem is s = 2λ_{\mathrm{min}}(Σ) \land 1.

Value

The solution s to the optimization problem defined above.

See Also

Other optimization: create.solve_asdp(), create.solve_sdp()

knockoff documentation built on Aug. 15, 2022, 9:06 a.m.