# sklearn.covariance.graphical_lasso¶

sklearn.covariance.graphical_lasso(emp_cov, alpha, cov_init=None, mode=’cd’, tol=0.0001, enet_tol=0.0001, max_iter=100, verbose=False, return_costs=False, eps=2.220446049250313e-16, return_n_iter=False)[source]

l1-penalized covariance estimator

Read more in the User Guide.

Parameters: emp_cov : 2D ndarray, shape (n_features, n_features) Empirical covariance from which to compute the covariance estimate. alpha : positive float The regularization parameter: the higher alpha, the more regularization, the sparser the inverse covariance. cov_init : 2D array (n_features, n_features), optional The initial guess for the covariance. mode : {‘cd’, ‘lars’} The Lasso solver to use: coordinate descent or LARS. Use LARS for very sparse underlying graphs, where p > n. Elsewhere prefer cd which is more numerically stable. tol : positive float, optional The tolerance to declare convergence: if the dual gap goes below this value, iterations are stopped. enet_tol : positive float, optional The tolerance for the elastic net solver used to calculate the descent direction. This parameter controls the accuracy of the search direction for a given column update, not of the overall parameter estimate. Only used for mode=’cd’. max_iter : integer, optional The maximum number of iterations. verbose : boolean, optional If verbose is True, the objective function and dual gap are printed at each iteration. return_costs : boolean, optional If return_costs is True, the objective function and dual gap at each iteration are returned. eps : float, optional The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. return_n_iter : bool, optional Whether or not to return the number of iterations. covariance : 2D ndarray, shape (n_features, n_features) The estimated covariance matrix. precision : 2D ndarray, shape (n_features, n_features) The estimated (sparse) precision matrix. costs : list of (objective, dual_gap) pairs The list of values of the objective function and the dual gap at each iteration. Returned only if return_costs is True. n_iter : int Number of iterations. Returned only if return_n_iter is set to True.

Notes

The algorithm employed to solve this problem is the GLasso algorithm, from the Friedman 2008 Biostatistics paper. It is the same algorithm as in the R glasso package.

One possible difference with the glasso R package is that the diagonal coefficients are not penalized.