MultiGroupRESIT

class lingam.MultiGroupRESIT(regressor, random_state=None, prior_knowledge=None, alpha=0.01)

Implementation of RESIT(regression with subsequent independence test) Algorithm [1] with multiple groups

References

[1] (1,2)

Jonas Peters, Joris M Mooij, Dominik Janzing, and Bernhard Sch ̈olkopf. Causal discovery with continuous additive noise models. Journal of Machine Learning Research, 15:2009-2053, 2014.

Notes

RESIT algorithm returns an adjacency matrix consisting of zeros or ones, rather than an adjacency matrix consisting of causal coefficients, in order to estimate nonlinear causality.

__init__(regressor, random_state=None, prior_knowledge=None, alpha=0.01)

Construct a RESIT model.

Parameters:

• regressor (regressor object implementing 'fit' and 'predict' function (default=None)) – Regressor to compute residuals. This regressor object must have fit method and predict function like scikit-learn’s model.

• random_state (int, optional (default=None)) – random_state is 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 [1]:

  • 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.

• alpha (float, optional (default=0.01)) – Alpha level for HSIC independence test when removing superfluous edges.

property adjacency_matrices_

Estimated adjacency matrices.

Returns:

adjacency_matrices_ – The list of adjacency matrix B for multiple datasets. The shape of B is (n_features, n_features), where n_features is the number of features.

Return type:

array-like, shape (B, …)

bootstrap(X_list, n_sampling)

Evaluate the statistical reliability of DAG based on the bootstrapping.

Parameters:

• X_list (array-like, shape (X, ...)) – Multiple datasets for training, where X is an dataset. The shape of ‘’X’’ is (n_samples, n_features), where n_samples is the number of samples and n_features is the number of features.

• n_sampling (int) – Number of bootstrapping samples.

Returns:

results – Returns the results of bootstrapping for multiple datasets.

Return type:

array-like, shape (BootstrapResult, …)

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)

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 – Because RESIT is a nonlinear algorithm, it cannot estimate the total effect and always returns a value of zero

Return type:

float

fit(X_list)

Fit the model to multiple datasets.

Parameters:

X_list (list, shape [X, ...]) – Multiple datasets for training, where X is an dataset. The shape of ‘’X’’ is (n_samples, n_features), where n_samples is the number of samples and n_features is the number of features.

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 – RESIT always returns a zero matrix

Return type:

array-like, shape (n_features, n_features)