Class UnconstrainedLASSOProblem


  • public class UnconstrainedLASSOProblem
    extends LMProblem
    A LASSO (least absolute shrinkage and selection operator) problem focuses on solving an RSS (residual sum of squared errors) problem with L1 regularization. The unconstrained form (Lagrangian form) solves \[ \min_w \left \{ 0.5 * \left \| Xw - y \right \|_2^2 + \lambda * \left \| w \right \|_1 \right \} \]
    See Also:
    • R. Tibshirani, "Regression shrinkage and selection via the LASSO," Journal of the Royal Statistical Society, Series B, Volume: 58, Issue: 1, 267 - 288, 1996.
    • Wikipedia: LASSO method
    • Constructor Detail

      • UnconstrainedLASSOProblem

        public UnconstrainedLASSOProblem​(Vector y,
                                         Matrix X,
                                         double lambda)
        Constructs a LASSO problem.
        Parameters:
        y - the vector of response variable (n * 1), properly demeaned and scaled
        X - the design matrix of factors (n * m), properly demeaned and scaled
        lambda - the penalization parameter
      • UnconstrainedLASSOProblem

        public UnconstrainedLASSOProblem​(UnconstrainedLASSOProblem that)
        Copy constructor.
        Parameters:
        that - another LASSOProblem
    • Method Detail

      • lambda

        public double lambda()
        Gets the penalization parameter for the unconstrained form of LASSO.
        Returns:
        lambda, the penalization parameter for the unconstrained form of LASSO