Ridge regression path computed through the singular value decomposition

Computes \((X^T X + k I_p)^{-1} X^T y = X^T (X X^T + k I_n)^{-1} y\) for every value in k. The singular value decomposition is computed once, so each additional value of k costs \(O(p r)\) operations with \(r = rank(X)\).

Usage

ridge_path(X, y, k, sv = NULL)

Arguments

X

prepared (centred/scaled) design matrix.

y

prepared response.

k

positive ridge parameters.

sv

optional precomputed output of the internal SVD helper.

Value

A p x length(k) matrix of ridge coefficients.