Inferring Boolean functions via higher-order correlations

Authors:
Markus Maucher;David V. Kracht;Steffen Schober;Martin Bossert;Hans A. Kestler
Affiliations:
Research group Bioinformatics and Systems Biology, Institute of Neural Information Processing, University of Ulm, Ulm, Germany 89069;Institute of Communications Engineering, University of Ulm, Ulm, Germany 89069;Institute of Communications Engineering, University of Ulm, Ulm, Germany 89069;Institute of Communications Engineering, University of Ulm, Ulm, Germany 89069;Research group Bioinformatics and Systems Biology, Institute of Neural Information Processing, University of Ulm, Ulm, Germany 89069
Venue:
Computational Statistics
Year:
2014

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Abstract

Both the Walsh transform and a modified Pearson correlation coefficient can be used to infer the structure of a Boolean network from time series data. Unlike the correlation coefficient, the Walsh transform is also able to represent higher-order correlations. These correlations of several combined input variables with one output variable give additional information about the dependency between variables, but are also more sensitive to noise. Furthermore computational complexity increases exponentially with the order. We first show that the Walsh transform of order 1 and the modified Pearson correlation coefficient are equivalent for the reconstruction of Boolean functions. Secondly, we also investigate under which conditions (noise, number of samples, function classes) higher-order correlations can contribute to an improvement of the reconstruction process. We present the merits, as well as the limitations, of higher-order correlations for the inference of Boolean networks.