ABICLiNGAM

class lingam.ABICLiNGAM(beta=1.0, lam=0.05, acyc_order=None, seed=0, max_outer=100, tol_h=1e-08, min_causal_effect=0.05, min_error_covariance=0.05, rho_max=1e+16, inner_start=1, inner_growth=1, inner_tol=0.0001)

Implementation of ABIC-LiNGAM Algorithm. [1] Original code: https://github.com/Yoshimitsu-try/ABIC_LiNGAM

References

[1]

Y. Morinishi and S. Shimizu. Differentiable causal discovery of linear non-Gaussian acyclic models under unmeasured confounding. Transactions on Machine Learning Research (TMLR), 2025.

__init__(beta=1.0, lam=0.05, acyc_order=None, seed=0, max_outer=100, tol_h=1e-08, min_causal_effect=0.05, min_error_covariance=0.05, rho_max=1e+16, inner_start=1, inner_growth=1, inner_tol=0.0001)

Construct a ABICLiNGAM model.

Parameters:

• beta (float, optional (default=1.0)) – Power in residual loss, i.e., ||r||^(2*beta)

• lam (float, optional (default=0.05)) – The weight of the regularization term.

• acyc_order (int or None, optional (default=None)) – Order of the truncated series for acyclicity penalty. If None, defaults to the number of variables.

• min_causal_effect (float, optional (default=0.05)) – Threshold for detecting causal edge. Causal edges with absolute values of causal effects less than min_causal_effect are excluded.

• min_error_covariance (float, optional (default=0.05)) – Threshold for detecting error covariances. Error covariances with absolute values less than min_error_covariance are excluded.

• seed (int, optional (default=0)) – Seed for the random number generator.

• max_outer (int, optional (default=100)) – Maximum number of outer iterations.

• tol_h (float, optional (default=1e-8)) – Tolerance for acyclicity penalty to stop.

• rho_max (float, optional (default=1e16)) – Maximum value for Augmented Lagrangian penalty parameter rho.

• inner_start (int, optional (default=1)) – Initial number of inner refinement steps.

• inner_growth (int, optional (default=1)) – Growth of inner refinement steps per outer iteration.

• inner_tol (float, optional (default=1e-4)) – Tolerance for inner loop convergence.

property adjacency_matrix_

Estimated adjacency matrix.

Returns:

adjacency_matrix_ – The adjacency matrix B of fitted model, where n_features is the number of features.

Return type:

array-like, shape (n_features, n_features)

bootstrap(X, n_sampling=100)

Bootstrap sampling to assess variability of estimates.

Parameters:

• X (array-like, shape (n_samples, n_features)) – Observed data matrix.

• n_sampling (int, optional (default=100)) – Number of bootstrap samples.

Returns:

• Bs (array-like, shape (n_sampling, n_features, n_features)) – Bootstrap samples of estimated adjacency matrices.

• Omegas (array-like, shape (n_sampling, n_features, n_features)) – Bootstrap samples of estimated error covariance matrices.

property causal_order_

Estimated causal ordering.

Returns:

causal_order_ – The causal order of fitted model, where n_features is the number of features.

Return type:

array-like, shape (n_features)

property coefficient_matrix_

Estimated coefficient matrix.

Returns:

coefficient_matrix_ – The coefficient matrix B of fitted model, where n_features is the number of features.

Return type:

array-like, shape (n_features, n_features)

property error_covariance_matrix_

Estimated error covariance matrix.

Returns:

error_covariance_matrix_ – The error covariance matrix Omega of fitted model, where n_features is the number of features.

Return type:

array-like, shape (n_features, n_features)

estimate_total_effect(X, from_index, to_index)

Estimate total effect using causal model.

Parameters:

• X (array-like, shape (n_samples, n_features)) – Original data, where n_samples is the number of samples and n_features is the number of features.

• from_index – Index of source variable to estimate total effect.

• to_index – Index of destination variable to estimate total effect.

Returns:

total_effect – Estimated total effect.

Return type:

float

fit(X)

Fit the model to X.

Parameters:

X (array-like, shape (n_samples, n_features)) – Observed data matrix.

Returns:

self – Returns the instance itself.

Return type:

object

get_error_independence_p_values(X)

Calculate the p-value matrix of independence between error variables.

Parameters:

X (array-like, shape (n_samples, n_features)) – Original data, where n_samples is the number of samples and n_features is the number of features.

Returns:

independence_p_values – p-value matrix of independence between error variables.

Return type:

array-like, shape (n_features, n_features)