make_sparse_model {natural}

Generate sparse linear model and random samples

Description

Generate design matrix and response following linear models y = X \beta + \epsilon, where \epsilon ~ N(0, \sigma^2), and X ~ N(0, \Sigma).

Usage

make_sparse_model(n, p, alpha, rho, snr, nsim)

Arguments

n

the sample size

p

the number of features

alpha

sparsity, i.e., n^\alpha nonzeros in the true regression coefficient.

rho

pairwise correlation among features

snr

signal to noise ratio, defined as \beta^T \Sigma \beta / \sigma^2

nsim

the number of simulations

Value

A list object containing:

x:

The n by p design matrix

y:

The n by nsim matrix of response vector, each column representing one replication of the simulation

beta:

The true regression coefficient vector

sigma:

The true error standard deviation