LiNGAM-based Methods

Estimation of Linear, Non-Gaussian Acyclic Model from observed data. It assumes non-Gaussianity of the noise terms in the causal model.

causal-learn has the official implementations for a set of LiNGAM-based methods (e.g., ICA-based LiNGAM 1, DirectLiNGAM 2, VAR-LiNGAM 3, RCD 4, and CAM-UV 5). And we are actively updating the list.

1

Shimizu, S., Hoyer, P. O., Hyvärinen, A., Kerminen, A., & Jordan, M. (2006). A linear non-Gaussian acyclic model for causal discovery. Journal of Machine Learning Research, 7(10).

2

Shimizu, S., Inazumi, T., Sogawa, Y., Hyvärinen, A., Kawahara, Y., Washio, T., … & Bollen, K. (2011). DirectLiNGAM: A direct method for learning a linear non-Gaussian structural equation model. The Journal of Machine Learning Research, 12, 1225-1248.

3

Hyvärinen, A., Zhang, K., Shimizu, S., & Hoyer, P. O. (2010). Estimation of a structural vector autoregression model using non-gaussianity. Journal of Machine Learning Research, 11(5).

4

Maeda, T. N., & Shimizu, S. (2020, June). RCD: Repetitive causal discovery of linear non-Gaussian acyclic models with latent confounders. In International Conference on Artificial Intelligence and Statistics (pp. 735-745). PMLR.

5

Maeda, T. N., & Shimizu, S. (2021). Causal Additive Models with Unobserved Variables. UAI.

ICA-based LiNGAM

from causallearn.search.FCMBased import lingam
model = lingam.ICALiNGAM(random_state, max_iter)
model.fit(X)

print(model.causal_order_)
print(model.adjacency_matrix_)

Parameters

random_state: int, optional (default=None). The seed used by the random number generator.

max_iter: int, optional (default=1000). The maximum number of iterations of FastICA.

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

Returns

model.causal_order_: array-like, shape (n_features). The causal order of fitted model, where n_features is the number of features.

model.adjacency_matrix_: array-like, shape (n_features, n_features). The adjacency matrix B of fitted model, where n_features is the number of features.

DirectLiNGAM

from causallearn.search.FCMBased import lingam
model = lingam.DirectLiNGAM(random_state, prior_knowledge, apply_prior_knowledge_softly, measure)
model.fit(X)

print(model.causal_order_)
print(model.adjacency_matrix_)

Parameters

random_state: int, optional (default=None). The seed used by the random number generator.

prior_knowledge: array-like, shape (n_features, n_features), optional (default=None). Prior knowledge used for causal discovery, where n_features is the number of features. The elements of prior knowledge matrix are defined as follows:

  • 0: \(x_i\) does not have a directed path to \(x_j\)

  • 1: \(x_i\) has a directed path to \(x_j\)

  • -1: No prior knowledge is available to know if either of the two cases above (0 or 1) is true.

apply_prior_knowledge_softly: boolean, optional (default=False). If True, apply prior knowledge softly.

measure: {‘pwling’, ‘kernel’}, optional (default=’pwling’). Measure to evaluate independence: ‘pwling’ or ‘kernel’.

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

Returns

model.causal_order_: array-like, shape (n_features). The causal order of fitted model, where n_features is the number of features.

model.adjacency_matrix_: array-like, shape (n_features, n_features). The adjacency matrix B of fitted model, where n_features is the number of features.

VAR-LiNGAM

from causallearn.search.FCMBased import lingam
model = lingam.VARLiNGAM(lags, criterion, prune, ar_coefs, lingam_model, random_state)
model.fit(X)

print(model.causal_order_)
print(model.adjacency_matrices_[0])
print(model.adjacency_matrices_[1])
print(model.residuals_)

Parameters

lags: int, optional (default=1). Number of lags.

criterion: {‘aic’, ‘fpe’, ‘hqic’, ‘bic’, None}, optional (default=’bic’). Criterion to decide the best lags within ‘lags’. Searching the best lags is disabled if ‘criterion’ is None.

prune: boolean, optional (default=False). Whether to prune the adjacency matrix or not.

ar_coefs: array-like, optional (default=None). Coefficients of AR model. Estimating AR model is skipped if specified ‘ar_coefs’. Shape must be (‘lags’, n_features, n_features).

lingam_model: lingam object inherits ‘lingam._BaseLiNGAM’, optional (default=None). LiNGAM model for causal discovery. If None, DirectLiNGAM algorithm is selected.

random_state: int, optional (default=None). ‘random_state’ is the seed used by the random number generator.

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

Returns

model.causal_order_: array-like, shape (n_features). The causal order of fitted model, where n_features is the number of features.

model.adjacency_matrices_: array-like, shape (lags, n_features, n_features). The adjacency matrix of fitted model, where n_features is the number of features.

model.residuals_: array-like, shape (n_samples). Residuals of regression, where n_samples is the number of samples.

RCD

from causallearn.search.FCMBased import lingam
model = lingam.RCD(max_explanatory_num, cor_alpha, ind_alpha, shapiro_alpha, MLHSICR, bw_method)
model.fit(X)

print(model.adjacency_matrix_)
print(model.ancestors_list_)

Parameters

max_explanatory_num: int, optional (default=2). Maximum number of explanatory variables.

cor_alpha: float, optional (default=0.01). Alpha level for pearson correlation.

ind_alpha: float, optional (default=0.01). Alpha level for HSIC.

shapiro_alpha: float, optional (default=0.01). Alpha level for Shapiro-Wilk test.

MLHSICR: bool, optional (default=False). If True, use MLHSICR for multiple regression, if False, use OLS for multiple regression.

bw_method: str, optional (default=’mdbs’). The method used to calculate the bandwidth of the HSIC.
  • ‘mdbs’: Median distance between samples.

  • ‘scott’: Scott’s Rule of Thumb.

  • ‘silverman’: Silverman’s Rule of Thumb.

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

Returns

model.adjacency_matrix_: array-like, shape (n_features, n_features). The adjacency matrix B of fitted model, where n_features is the number of features.

model.ancestors_list_: array-like, shape (n_features). The list of causal ancestors sets, where n_features is the number of features.

CAM-UV

from causallearn.search.FCMBased.lingam import CAMUV
P, U = CAMUV.execute(data, alpha, num_explanatory_vals)

for i, result in enumerate(P):
    if not len(result) == 0:
        print("child: " + str(i) + ",  parents: " + str(result))

for result in U:
    print(result)

Parameters

data: array-like, shape (n_samples, n_features). Training data, where n_samples is the number of samples and n_features is the number of features.

alpha: the alpha level for independence testing.

num_explanatory_vals: the maximum number of variables to infer causal relationships. This is equivalent to d in the paper.

Returns

P: P[i] contains the indices of the parents of Xi.

U: The indices of variable pairs having UCPs or UBPs.