Class CovarianceSelectionProblem


  • public class CovarianceSelectionProblem
    extends Object
    This class defines the covariance selection problem outlined in d'Aspremont (2008). This technique is first used in Dempster (1972) and has some recent advancement, see for instance, Banerjee et al. (2007).
    See Also:
    • A. d'Aspremont, "Identifying small mean reverting portfolios," Working Paper, 2008.
    • A. Dempster, "Covariance selection," Biometrics, Volume: 28, 157 - 175, 1972.
    • Constructor Detail

      • CovarianceSelectionProblem

        public CovarianceSelectionProblem​(Matrix S,
                                          double t)
        Constructs a covariance selection problem.
        Parameters:
        S - a sample covariance (or correlation) matrix
        t - the penalization parameter t for L1 regularization
      • CovarianceSelectionProblem

        public CovarianceSelectionProblem​(MultivariateTimeSeries ts,
                                          double t,
                                          boolean isCor)
        Constructs a covariance selection problem from a multivariate time series.
        Parameters:
        ts - a multivariate time series
        t - the penalization parameter t for L1 regularization
        isCor - indicator of whether sample correlation matrix is used instead of the covariance matrix
      • CovarianceSelectionProblem

        public CovarianceSelectionProblem​(MultivariateTimeSeries ts,
                                          double t)
        Constructs a covariance selection problem from a multivariate time series. By default, the sample covariance matrix is used in the calculation.
        Parameters:
        ts - a multivariate time series
        t - the penalization parameter t for L1 regularization
      • CovarianceSelectionProblem

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

      • S

        public ImmutableMatrix S()
        Gets the original sample covariance matrix.
        Returns:
        the original sample covariance matrix
      • t

        public double t()
        Gets the penalization parameter t for L1 regularization.
        Returns:
        the penalization parameter t for L1 regularization
      • penalizedL1

        public double penalizedL1​(Matrix X)
        Gets the value of an L1-penalized function.
        Parameters:
        X - the inverse of a covariance matrix (to be estimated)
        Returns:
        the value of an L1-penalized function
      • penalizedCardinality

        public double penalizedCardinality​(Matrix X)
        Gets the value of a cardinality-penalized function.
        Parameters:
        X - the inverse of a covariance matrix (to be estimated)
        Returns:
        the value of a cardinality-penalized function