LongitudinalRESIT

class lingam.LongitudinalRESIT(regressor, n_lags=1, prior_knowledge=None, prior_knowledge_lag=None, alpha=0.01, is_common_graph=True)

Implementation of RESIT(regression with subsequent independence test) Algorithm [1] for longitudinal data

References

[1]

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.

property A_list_

Estimated lag causal graphs.

If is_common_graph=True, a list of length 1. If is_common_graph=False, a list of length T; A_list_[0], …, A_list_[n_lags-1] are NaN tensors. Each element has shape (n_lags, n_vars, n_vars). A_list_[t][k, j, i] = 1 means there is an edge from variable i at k+1 time steps before time t to variable j at time t (k is 0-origin).

Returns:

A_list_

Return type:

list of ndarray

property B_list_

Estimated instantaneous causal graphs.

If is_common_graph=True, a list of length 1 (shared across all time points). If is_common_graph=False, a list of length T; B_list_[0], …, B_list_[n_lags-1] are NaN matrices. Each element has shape (n_vars, n_vars). B_list_[t][j, i] = 1 means there is an edge from variable i to variable j.

Returns:

B_list_

Return type:

list of ndarray

__init__(regressor, n_lags=1, prior_knowledge=None, prior_knowledge_lag=None, alpha=0.01, is_common_graph=True)

Construct a LongitudinalRESIT 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.

• n_lags (int, optional (default=1)) – Number of lags (past time points) to use. Must be an integer >= 1.

• prior_knowledge (array-like, optional (default=None)) – Prior knowledge used for the instantaneous causal graph, assuming a common causal structure across all time points. A single matrix of shape (n_vars, n_vars). Values: 0=no edge, 1=edge exists, -1=unknown.

• prior_knowledge_lag (array-like, optional (default=None)) – Prior knowledge used for the lag causal graph, assuming a common causal structure across all time points. A single tensor of shape (n_lags, n_vars, n_vars). Values: 0=no edge, 1=edge exists, -1=unknown.

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

• is_common_graph (bool, optional (default=True)) – If True, estimate a single causal graph shared across all time points. If False, estimate an independent causal graph for each time point.

property adjacency_matrices_

Estimated adjacency matrices combining instantaneous and lag graphs.

If is_common_graph=True, a list of length 1. If is_common_graph=False, a list of length T; adjacency_matrices_[0], …, adjacency_matrices_[n_lags-1] are NaN matrices. Each element has shape (n_vars, n_vars*(n_lags+1)). The first n_vars columns correspond to the instantaneous graph B, and the next n_vars columns correspond to A[0], and so on.

Returns:

adjacency_matrices_

Return type:

list of ndarray

bootstrap(X_list, n_sampling)

Evaluate the statistical reliability of DAG based on the bootstrapping.

Parameters:

• X_list (list of ndarray, shape [(n_samples, n_vars), ...]) – Multiple datasets for training, where each dataset corresponds to a time point. The length of X_list is T (number of time points). T >= 2 is required.

• n_sampling (int) – Number of bootstrapping samples.

Returns:

results – Returns the results of bootstrapping for multiple datasets.

Return type:

LongitudinalRESITBootstrapResult

property causal_order_

Instantaneous causal order common to all time points.

Returns:

causal_order_ – The causal order of the fitted model, where the first element is the most upstream variable and the last is the sink.

Return type:

list of int

fit(X_list)

Fit the model to X_list.

Parameters:

X_list (list of ndarray, shape [(n_samples, n_vars), ...]) – Multiple datasets for training, where each dataset corresponds to a time point. The length of X_list is T (number of time points). T >= 2 is required.

Returns:

self – Returns the instance itself.

Return type:

object