Ridge regression

Ridge regression is a modification of the standard least-squares problem which instead solves

\[\min_X \| \text{op}(A) X - B \|_2^2 + \| \alpha X \|_2^2,\]

which is a special case of Tikhonov regularization where the weighting matrix is a multiple of the identity.

C++ API

type RidgeAlg

An enum that can take on the values:

• RIDGE_CHOLESKY: Run a less accurate, but often faster, Cholesky-based algorithm

• RIDGE_QR: Run a QR-based algorithm

• RIDGE_SVD: Run an SVD-based algorithm

void Ridge(const Matrix<F> &A, const Matrix<F> &B, Base<F> alpha, Matrix<F> &X, RidgeAlg alg = RIDGE_CHOLESKY)

void Ridge(const AbstractDistMatrix<F> &A, const AbstractDistMatrix<F> &B, Base<F> alpha, AbstractDistMatrix<F> &X, RidgeAlg alg = RIDGE_CHOLESKY)

C API

ElRidgeAlg

An enum that can take on the values:

• EL_RIDGE_CHOLESKY: Run a less accurate, but often faster, Cholesky-based algorithm

• EL_RIDGE_QR: Run a QR-based algorithm

• EL_RIDGE_SVD: Run an SVD-based algorithm

ElError ElRidge_s(ElConstMatrix_s A, ElConstMatrix_s B, float alpha, ElMatrix_s X, ElRidgeAlg alg)

ElError ElRidge_d(ElConstMatrix_d A, ElConstMatrix_d B, double alpha, ElMatrix_d X, ElRidgeAlg alg)

ElError ElRidge_c(ElConstMatrix_c A, ElConstMatrix_c B, float alpha, ElMatrix_c X, ElRidgeAlg alg)

ElError ElRidge_z(ElConstMatrix_z A, ElConstMatrix_z B, double alpha, ElMatrix_z X, ElRidgeAlg alg)

ElError ElRidgeDist_s(ElConstDistMatrix_s A, ElConstDistMatrix_s B, float alpha, ElDistMatrix_s X, ElRidgeAlg alg)

ElError ElRidgeDist_d(ElConstDistMatrix_d A, ElConstDistMatrix_d B, double alpha, ElDistMatrix_d X, ElRidgeAlg alg)

ElError ElRidgeDist_c(ElConstDistMatrix_c A, ElConstDistMatrix_c B, float alpha, ElDistMatrix_c X, ElRidgeAlg alg)

ElError ElRidgeDist_z(ElConstDistMatrix_z A, ElConstDistMatrix_z B, double alpha, ElDistMatrix_z X, ElRidgeAlg alg)