LongitudinalLiNGAM

class lingam.LongitudinalLiNGAM(n_lags=1, measure='pwling', random_state=None)

Implementation of Longitudinal LiNGAM algorithm [1]

References

[1]

K. Kadowaki, S. Shimizu, and T. Washio. Estimation of causal structures in longitudinal data using non-Gaussianity. In Proc. 23rd IEEE International Workshop on Machine Learning for Signal Processing (MLSP2013), pp. 1–6, Southampton, United Kingdom, 2013.

__init__(n_lags=1, measure='pwling', random_state=None)

Construct a model.

Parameters:

• n_lags (int, optional (default=1)) – Number of lags.

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

• random_state (int, optional (default=None)) – random_state is the seed used by the random number generator.

property adjacency_matrices_

Estimated adjacency matrices.

Returns:

adjacency_matrices_ – The list of adjacency matrix B(t,t) and B(t,t-τ) for longitudinal datasets. The shape of B(t,t) and B(t,t-τ) is (n_features, n_features), where n_features is the number of features. If the previous data required for the calculation are not available, such as B(t,t) or B(t,t-τ) at t=0, all elements of the matrix are nan.

Return type:

array-like, shape ((B(t,t), B(t,t-1), …, B(t,t-τ)), …)

bootstrap(X_list, n_sampling, start_from_t=1)

Evaluate the statistical reliability of DAG based on the bootstrapping.

Parameters:

• X_list (array-like, shape (X, ...)) – Longitudinal 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_orders_

Estimated causal ordering.

Returns:

causal_order_ – The causal order of fitted models for B(t,t). The shape of causal_order is (n_features), where n_features is the number of features.

Return type:

array-like, shape (causal_order, …)

estimate_total_effect(X_t, from_t, from_index, to_t, to_index)

Estimate total effect using causal model.

Parameters:

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

• _t (from) – The timepoint of source variable.

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

• to_t – The timepoint of destination variable.

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

Returns:

total_effect – Estimated total effect.

Return type:

float

estimate_total_effect2(from_t, from_index, to_t, to_index)

Estimate total effect using causal model.

Parameters:

• _t (from) – The timepoint of source variable.

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

• to_t – The timepoint of destination variable.

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

Returns:

total_effect – Estimated total effect.

Return type:

float

fit(X_list)

Fit the model to datasets.

Parameters:

X_list (list, shape [X, ...]) – Longitudinal 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()

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 E is an dataset. The shape of E is (n_samples, n_features), where n_samples is the number of samples and n_features is the number of features.

Return type:

list, shape [E, …]