# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.covariance.covarianceselection.lasso

## Class CovarianceSelectionGLASSOFAST

• java.lang.Object
• com.numericalmethod.suanshu.stats.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.
• "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

All Methods
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