make_sparse_model function

Generate sparse linear model and random samples

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

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

Returns

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