VARMA-LiNGAM

class lingam.VARMALiNGAM(order=(1, 1), criterion='bic', prune=True, max_iter=100, ar_coefs=None, ma_coefs=None, lingam_model=None, random_state=None)

Implementation of VARMA-LiNGAM Algorithm [1]

References

[1]

Yoshinobu Kawahara, Shohei Shimizu, Takashi Washio. Analyzing relationships among ARMA processes based on non-Gaussianity of external influences. Neurocomputing, Volume 74: 2212-2221, 2011

__init__(order=(1, 1), criterion='bic', prune=True, max_iter=100, ar_coefs=None, ma_coefs=None, lingam_model=None, random_state=None)

Construct a VARMALiNGAM model.

Parameters:

• order (turple, length = 2, optional (default=(1, 1))) – Number of lags for AR and MA model.

• criterion ({'aic', 'bic', 'hqic', None}, optional (default='bic')) – Criterion to decide the best order in the all combinations of order. Searching the best order is disabled if criterion is None.

• prune (boolean, optional (default=True)) – Whether to prune the adjacency matrix of lags.

• max_iter (int, optional (default=100)) – Maximm number of iterations to estimate VARMA model.

• ar_coefs (array-like, optional (default=None)) – Coefficients of AR of ARMA. Estimating ARMA model is skipped if specified ar_coefs and ma_coefs. Shape must be (order[0], n_features, n_features).

• ma_coefs (array-like, optional (default=None)) – Coefficients of MA of ARMA. Estimating ARMA model is skipped if specified ar_coefs and ma_coefs. Shape must be (order[1], 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.

property adjacency_matrices_

Estimated adjacency matrix.

Returns:

adjacency_matrices_ – The adjacency matrix psi and omega of fitted model, where n_features is the number of features.

Return type:

array-like, shape ((p, n_features, n_features), (q, n_features, n_features))

bootstrap(X, n_sampling)

Evaluate the statistical reliability of DAG based on the bootstrapping.

Parameters:

• 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.

• n_sampling (int) – Number of bootstrapping samples.

Returns:

result – Returns the result of bootstrapping.

Return type:

TimeseriesBootstrapResult

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, E, from_index, to_index, from_lag=0)

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.

• E (array-like, shape (n_samples, n_features)) – Original error 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

estimate_total_effect2(n_features, from_index, to_index, from_lag=0)

Estimate total effect using causal model.

Parameters:

• n_features – 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)) – Training data, 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()

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

Returns:

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

Return type:

array-like, shape (n_features, n_features)

property residuals_

Residuals of regression.

Returns:

residuals_ – Residuals of regression, where n_samples is the number of samples.

Return type:

array-like, shape (n_samples)