Graph model selection

Tuning rules for graphical models. The headline export is ebic_path, the field-standard Extended Bayesian Information Criterion (Foygel & Drton 2010) for single-population graphical lasso. The joint analogue (joint_ebic_path) sums per-population log-likelihoods and counts the union of active edges across populations.

EBIC

The EBIC formula for a single-population precision estimate Θ̂(α) is

\[ \text{EBIC}(\alpha) = -2\,\hat\ell\,(\hat\Theta(\alpha); S) + |\hat E(\alpha)| \log n + 4\gamma|\hat E(\alpha)| \log p, \]

where |Ê(α)| is the number of nonzero off-diagonal entries and γ ∈ [0, 1] controls the strength of the EBIC correction. γ = 0 gives plain BIC. γ = 0.5 is the field default for graphical models and the value bootnet / qgraph use out of the box.

skein_glm.graph_selection.ebic_path(X, estimator_cls, lambdas, *, gamma=0.5, n=None, assume_centered=False, **estimator_kwargs)[source]

Sweep a λ-grid for a graphical estimator and pick the model minimising EBIC.

Parameters:

  • X (ndarray) – Either raw (n, p) data or a precomputed (p, p) symmetric covariance. If precomputed, pass n explicitly.

  • estimator_cls (a class with an `alpha parameter (GraphicalLasso,`) – GraphicalMCP, GraphicalSCAD).

  • lambdas (array-like of floats (positive, ideally in descending order).)

  • gamma (float, default 0.5) – EBIC strength. 0 → BIC.

  • n (int, optional) – Effective sample size. Required if X is precomputed covariance.

  • assume_centered (bool, default False)

  • **estimator_kwargs (passed through to the estimator constructor.)

Return type:

EBICPathResult

class skein_glm.graph_selection.EBICPathResult(best_estimator, best_lambda, best_ebic, lambdas, ebic, n_edges)[source]

Bases: object

Outcome of a single-population EBIC search.

Parameters:
best_estimator
Type:

fitted estimator at the EBIC-selected λ.

best_lambda
Type:

float

best_ebic
Type:

float

lambdas
Type:

ndarray (n_lambdas,)

ebic
Type:

ndarray (n_lambdas,)

n_edges
Type:

ndarray (n_lambdas,) int

skein_glm.graph_selection.joint_ebic_path(Xs, estimator_cls, lambdas, *, gamma=0.5, ns=None, assume_centered=False, **estimator_kwargs)[source]

EBIC tuner for joint glasso. Walks a λ_2 grid; the active edge count is the union across populations (an edge counts once if any population has it nonzero).

Sums per-population log-likelihoods. Per-pop n_k is read from raw X^(k) row count, or via the ns argument when populations are passed as precomputed covariances.

Parameters:
Return type:

JointEBICPathResult

class skein_glm.graph_selection.JointEBICPathResult(best_estimator: 'Any', best_lambda_2: 'float', best_ebic: 'float', lambdas: 'NDArray[np.float64]', ebic: 'NDArray[np.float64]', n_edges_union: 'NDArray[np.int64]')[source]

Bases: object

Parameters: