Logistic regression

Given a sequence of vectors \(\{a_i\}_{i=0}^{n-1} \subset \mathbb{R}^m\) with binary labels \(\{\eta_i\}_{i=0}^{n-1} \subset \{0,1\}\), \(\ell_p\)-regularized logistic regression solves the problem

\[\min_{z,\nu} \frac{1}{n} \sum_{i=0}^{n-1} f(z^H a_i + \nu \eta_i) + \lambda \| z \|_p,\]

where \(f\) is the logistic loss function,

\[f(t) = \log(1+e^{-t}).\]

Note

While sometimes functional, this implementation is still very much a work-in-progress.

C++ API

Regularization

An enum which can take on the values NO_PENALTY, L1_PENALTY, and L2_PENALTY

Int LogisticRegression(const Matrix<Real> &G, const Matrix<Real> &q, Matrix<Real> &z, Real gamma, Regularization penalty = L1_PENALTY, Real rho = 1, Int maxIter = 500, bool inv = true, bool progress = true)

Int LogisticRegression(const ElementalMatrix<Real> &G, const ElementalMatrix<Real> &q, ElementalMatrix<Real> &z, Real gamma, Regularization penalty = L1_PENALTY, Real rho = 1, Int maxIter = 500, bool inv = true, bool progress = true)

C API

ElRegularization

An enum which can take on the values EL_NO_PENALTY, EL_L1_PENALTY, and EL_L2_PENALTY

ElError ElLogisticRegression_s(ElConstMatrix_s G, ElConstMatrix_s q, ElMatrix_s z, float gamma, ElRegularization penalty, ElInt* numIts)

ElError ElLogisticRegression_d(ElConstMatrix_d G, ElConstMatrix_d q, ElMatrix_d z, double gamma, ElRegularization penalty, ElInt* numIts)

ElError ElLogisticRegressionDist_s(ElConstDistMatrix_s G, ElConstDistMatrix_s q, ElDistMatrix_s z, float gamma, ElRegularization penalty, ElInt* numIts)

ElError ElLogisticRegressionDist_d(ElConstDistMatrix_d G, ElConstDistMatrix_d q, ElDistMatrix_d z, double gamma, ElRegularization penalty, ElInt* numIts)