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Last updated: 2019-10-14

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Results

MR.ASH vs penalized linear regression

This is for MR.ASH vs. penalized linear regression.

Our story is

the MR.ASH’s shrinkage operator (from a normal mixture prior) is more flexible than other popular shrinkage operators, which is a parametric form of $\lambda$ (and $\gamma$ if exists).
VEB can do better than cross validation.

Performance of methods – Ridge case

Result 1

Flexibility of convex/non-convex shrinkage operators (E-NET, SCAD, MCP, L0Learn) vs MR.ASH shrinkage operator.

Result 2

MR.ASH vs. all other methods.

This is to reproduce the results in the Experiment section. Throughout the studies, we will fix $n = 500$ .

The default setting is (1) The number of coefficients $p = 2000$ (2) The number of nonzero coefficients $s = 20$ (sparsity) (3) Design: IndepGauss (4) Signal shape for nonzero coefficients: SparseNormal (5) PVE: 0.5

We will change exactly one of the below and fix the rest.

$p$ Sparsity Design PVE