Causal Information Approach to Partial Conditioning in Multivariate Data Sets

Abstract

When evaluating causal influence from one time series to another in a multivariate data set it is necessary to take into account the conditioning effect of the other variables. In the presence of many variables and possibly of a reduced number of samples, full conditioning can lead to computational and numerical problems. In this paper, we address the problem of partial conditioning to a limited subset of variables, in the framework of information theory. The proposed approach is tested on simulated data sets and on an example of intracranial EEG recording from an epileptic subject. We show that, in many instances, conditioning on a small number of variables, chosen as the most informative ones for the driver node, leads to results very close to those obtained with a fully multivariate analysis and even better in the presence of a small number of samples. This is particularly relevant when the pattern of causalities is sparse.

Compensated Transfer Entropy as a Tool for Reliably Estimating Information Transfer in Physiological Time Series

“…Therefore, future studies should aim at integrating within our framework recently proposed approaches for the inference of the direction of instantaneous causality based on data structure rather than on prior assumptions [17,23]. Another interesting development would be to combine together the approach for partial conditioning recently proposed in [46], which selects the most informative subset of processes for describing the source process, with our nonuniform embedding procedure, which selects the most informative subset of lagged variables for describing the target process. Such an integrated approach for dimensionality reduction would further favor the development of a fully multivariate efficient TE estimator.…”

Transfer entropy in continuous time, with applications to jump and neural spiking processes

“…Indeed, transfer entropy has proven particularly popular in computational neuroscience for characterizing neural information flows, with applications such as inferring effective neural information networks underpinning cognitive tasks and their variation [10][11][12][13][14], across data modalities including magnetoencephalography (MEG) [15,16], electroencephalography (EEG) [17][18][19], and functional magnetic resonance imaging (fMRI) [20,21]. Applications to spike train data have been less abundant, however.…”

Mapping the epileptic brain with EEG dynamical connectivity: Established methods and novel approaches

“…Barnett et al [53] have shown that under the assumption of Gaussian distribution of the variables Granger causality is equivalent to Transfer Entropy (TE), a model-free measure of directed connectivity [54]. This result has been used to optimize Granger causality analysis to infer connectivity in high dimensional datasets, as those encountered in epilepsy analysis, in [55]. Connectivity patterns in the epileptic brain obtained by TE are reported in [56], [57] and [58].…”