L2Solver

class L2Solver(regularizer=0)

Solve the l2-norm ordinary least-squares problem with L2 regularization:

sum_{i} min_{x_i} ||Ax_i - b_i||_2^2 + ||λx_i||_2^2, λ ≥ 0,

or, written in the Frobenius norm,

min_{X} ||AX - B||_F^2 + ||λX||_F^2, λ ≥ 0.

The solution is calculated using the singular value decomposition of A: If A = U Σ V^T, then X = V Σinv(λ) U^T B, where Σinv(λ)[i, i] = Σ[i, i] / (Σ[i, i]^2 + λ^2).

Properties

A	Left-hand side data matrix.
B	"Right-hand side matrix B = [ b_1 | .
d	Number of unknowns to learn in each problem (number of columns of A).
k	Number of equations in the least-squares problem (number of rows of A).
r	Number of independent least-squares problems (number of columns of B).
regularizer	Regularization scalar, matrix, or list of these.

Methods

cond	Calculate the 2-norm condition number of the data matrix A.
fit	Take the SVD of A in preparation to solve the least-squares problem.
misfit	Calculate the data misfit (residual) of the non-regularized problem for each column of B = [ b_1 | .
predict	Solve the regularized least-squares problem.
regcond	Compute the 2-norm condition number of the regularized data matrix.
residual	Calculate the residual of the regularized problem for each column of B = [ b_1 | .