dev.nm.stat.covariance.covarianceselection.lasso

Class CovarianceSelectionGLASSOFAST

java.lang.Object

dev.nm.stat.covariance.covarianceselection.lasso.CovarianceSelectionGLASSOFAST

All Implemented Interfaces:

CovarianceSelectionSolver

public class CovarianceSelectionGLASSOFAST
extends Object
implements CovarianceSelectionSolver

GLASSOFAST is the Graphical LASSO algorithm to solve the covariance selection problem. The covariance selection problem is formulated as this: \[ \max_{X} \log(\det X) - Tr(\Sigma X)-\rho Card(X) \] in the variable of \(X \in S^n\), where \(\Sigma \in S^n\) is the sample covariance matrix, \(Card(X)\) the cardinality of \(X\), i.e., the number of non-zero coefficients in \(X\). \(\rho > 0\) is a parameter controlling the tradeoff between the likelihood and structure.

See Also:

• "Sustik, M.A. and Calderhead, B., "GLASSOFAST: An efficient GLASSO implementation," UTCS Technical Report TR-12-29, November 6, 2012."
• "A. d'Aspremont, "Identifying Small Mean Reverting Portfolios", 2008."
• "O. Banerjee, L. E. Ghaoui and A. d'Aspremont, "Model Selection Through Sparse Maximum Likelihood Estimation for multivariate Gaussian or Binary Data," Journal of Machine Learning Research, 9, pp. 485-516, March 2008."

Constructor Summary

Constructors

Constructor and Description
CovarianceSelectionGLASSOFAST(CovarianceSelectionProblem problem) Solves the maximum likelihood problem for covariance selection.

Method Summary

Modifier and Type	Method and Description
Matrix	covariance() Gets the estimated covariance matrix.
Matrix	inverseCovariance() Gets the inverse of the estimated covariance matrix.
boolean	isConverged() Checks if the algorithm converges.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

CovarianceSelectionGLASSOFAST

public CovarianceSelectionGLASSOFAST(CovarianceSelectionProblem problem)

Solves the maximum likelihood problem for covariance selection.

Parameters:

problem - the covariance selection problem

Method Detail

covariance

public Matrix covariance()

Gets the estimated covariance matrix.

Specified by:

covariance in interface CovarianceSelectionSolver

Returns:

the estimated covariance matrix

inverseCovariance

public Matrix inverseCovariance()

Gets the inverse of the estimated covariance matrix.

Specified by:

inverseCovariance in interface CovarianceSelectionSolver

Returns:

the inverse of the estimated covariance matrix

isConverged

public boolean isConverged()

Checks if the algorithm converges.

Returns:

true if the algorithm stops before maximum iteration is reached