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, RCD 3, and CAM-UV 4). 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
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.
- 4
Maeda, T. N., & Shimizu, S. (2021). Causal Additive Models with Unobserved Variables. UAI.
ICA-based LiNGAM
from causal-learn.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.
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. Set np.nan if order is unknown.
DirectLiNGAM
from causal-learn.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’.
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. Set np.nan if order is unknown.
RCD
from causal-learn.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_)
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.
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. Set np.nan if order is unknown.
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 causal-learn.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
X: matrixs.
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.