TransferEntropyPT: An R Package to Assess
Transfer Entropies via Permutation TestsPatrick Boba and Kay Hamacher(B)Technische Universit ̈at Darmstadt, Darmstadt, Germany
[email protected]Abstract.The packageTransferEntropyPTprovidesRfunctions to
calculate the transfer entropy (TE) [ 6 ] for time series of (binned) data.
The package provides a function to assess the statistical significance of
the TE using permutation tests on the sequential data of the time series.
The underlying code base is written inC++for computational efficiency
and makes use of theboostandOpenMPlibraries for parallelization of
the data-parallel tasks in the permutation tests. In addition top-values
from hypothesis tests on independence, the package provides direct access
to the percentiles themselves. An anticipatory toy model, as well as a
biological network is used as show cases. Here, every time series concen-
trations of a single molecular species is tested and assessed against each
other.1 Introduction
A potential interdependence of two random variables can be analyzed by a vari-
ety of measures. Among the classical ones, we find Pearson’s correlation coeffi-
cient or the mutual information. The Transfer Entropy (TE) introduced in [ 6 ]
overcomes some of the shortcomings of these traditional measures when applied
to time series data, such as only being able to identify linear correlations. To this
end, TE employs conditional probabilities with respect to the specific time order
of events in a time series. In recent years, TE has gained traction in many appli-
cations, e.g. the analysis of gene regulatory networks [ 7 ] or analysis procedures
for magnetoencephalography in neuroscience [ 9 ]. Furthermore, Bauer et al. [ 1 ]
were able to show the causal relationship between perturbations in process vari-
ables such as pressure of chemical processes. At present, there is no software
package readily available to compute the TEand assess its significance in sta-
tistical software systems likeR. The growth in the number of TE applications
prompted us to adapt previous work [ 2 ] as a package explicitly for the statistical
softwareR.
1.1 Background: Information Theory
First, we want to review some basic concepts of information theory to illus-
trate the issues the package addresses. TheKullback-Leibler-Divergencemea-
sures the amount of information needed (in bits) to get from the distribution
©cSpringer International Publishing AG 2017
J. Feret and H. Koeppl (Eds.): CMSB 2017, LNBI 10545, pp. 285–290, 2017.
DOI: 10.1007/978-3-319-67471-1 17