Class ConstrainedLASSObyLARS

  • All Implemented Interfaces:
    LinearModel

    public class ConstrainedLASSObyLARS
    extends Object
    implements LinearModel
    This class solves the constrained form of LASSO by modified least angle regression (LARS) and linear interpolation: \[ \min_w \left \{ \left \| Xw - y \right \|_2^2 \right \}\) subject to \( \left \| w \right \|_1 \leq t \]
    See Also:
    • B. Efron et. al, "Least Angle Regression," The Annals of Statistics, Volume: 32(2), 407 - 499, 2004.
    • T. Hastie, R. Tibshirani and J. Friedman, "The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Second Edition)," New York, Springer-Verlag, 2009.
    • Wikipedia: LASSO method
    • Constructor Detail

      • ConstrainedLASSObyLARS

        public ConstrainedLASSObyLARS​(ConstrainedLASSOProblem problem,
                                      boolean demeaned,
                                      boolean normalized,
                                      double epsilon,
                                      int maxIterations)
        Solves a constrained LASSO problem by modified least angle regression (LARS) and linear interpolation.
        Parameters:
        problem - a constrained LASSO problem
        demeaned - an indicator of whether an intercept is included in the model
        normalized - an indicator of whether the predictors are first normalized to have unit L2 norm
        epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0
        maxIterations - the maximum number of iterations
      • ConstrainedLASSObyLARS

        public ConstrainedLASSObyLARS​(ConstrainedLASSOProblem problem)
        Solves a constrained LASSO problem by modified least angle regression (LARS) and linear interpolation.
        Parameters:
        problem - a constrained LASSO problem
    • Method Detail

      • Ey

        public double Ey​(Vector x)
        Description copied from interface: LinearModel
        Computes the expectation \(E(y(x))\) given an input.
        Specified by:
        Ey in interface LinearModel
        Parameters:
        x - an input
        Returns:
        \(E(y(x))\)
      • beta

        public LMBeta beta()
        Description copied from interface: LinearModel
        Gets \(\hat{\beta}\) and statistics.
        Specified by:
        beta in interface LinearModel
        Returns:
        \(\hat{\beta}\) and statistics
      • residuals

        public LMResiduals residuals()
        Description copied from interface: LinearModel
        Gets the residual analysis of an OLS regression.
        Specified by:
        residuals in interface LinearModel
        Returns:
        the residual analysis