skglm.AdaptiveGraphicalLasso

class skglm.AdaptiveGraphicalLasso(alpha=1.0, eps=1e-10, n_reweights=5, max_iter=1000, tol=1e-08, warm_start=False, penalty=<skglm.penalties.separable.L0_5 object>, verbose=False)

Adaptive version of the Graphical Lasso with non-convex penalties.

Solves non-convex penalty variations using an iterative reweighting strategy (Candès et al., 2007).

At each reweighting iteration, it solves

`\Theta^* = \underset{\Theta \succ 0}{\arg\min}\ -\log\det(\Theta) + \langle S, \Theta \rangle + \alpha \sum_{i \ne j} w_{ij}^{(k)} |\Theta_{ij}|`

where the weights are updated as

`w_{ij}^{(k)} = \frac{1}{\epsilon} \quad \text{if } \Theta_{ij}^{(k-1)} = 0`

`w_{ij}^{(k)} = |p'(\Theta_{ij}^{(k-1)})| \quad \text{otherwise}`

where `p'(\cdot)` is the derivative of the non-convex penalty function.

Parameters:

alphafloat, default=1.0

Regularization parameter controlling sparsity.

epsfloat, default=1e-10

Small value for handling exactly zero elements in reweighting. Controls numerical stability of the adaptive algorithm.

n_reweightsint, default=5

Number of reweighting iterations.

max_iterint, default=1000

Maximum iterations for inner solver.

tolfloat, default=1e-8

Convergence tolerance.

warm_startbool, default=False

Whether to use warm start.

penaltyPenalty object, default=L0_5(1.)

Non-convex penalty function. Must have a ‘derivative’ method. The penalty’s alpha parameter should typically match this class’s alpha.

verbosebool, default=False

Whether to print verbose output.

Attributes:

precision_ndarray

Estimated precision (inverse covariance) matrix.

covariance_ndarray

Estimated covariance matrix.

n_iter_int

Number of iterations run.

References

[1]

Candès et al., 2007.

__init__(alpha=1.0, eps=1e-10, n_reweights=5, max_iter=1000, tol=1e-08, warm_start=False, penalty=<skglm.penalties.separable.L0_5 object>, verbose=False)

Methods

__init__([alpha, eps, n_reweights, ...])
fit(X[, y, mode])	Fit the AdaptiveGraphicalLasso model.
get_metadata_routing()	Get metadata routing of this object.
get_params([deep])	Get parameters for this estimator.
set_fit_request(*[, mode])	Configure whether metadata should be requested to be passed to the fit method.
set_params(**params)	Set the parameters of this estimator.