Measuring multivariate redundant information with pointwise common change in surprisal

Ince, R. A.A. (2017) Measuring multivariate redundant information with pointwise common change in surprisal. Entropy, 19(7), 318. (doi:10.3390/e19070318)

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Abstract

The problem of how to properly quantify redundant information is an open question that has been the subject of much recent research. Redundant information refers to information about a target variable S that is common to two or more predictor variables Xi . It can be thought of as quantifying overlapping information content or similarities in the representation of S between the Xi . We present a new measure of redundancy which measures the common change in surprisal shared between variables at the local or pointwise level. We provide a game-theoretic operational definition of unique information, and use this to derive constraints which are used to obtain a maximum entropy distribution. Redundancy is then calculated from this maximum entropy distribution by counting only those local co-information terms which admit an unambiguous interpretation as redundant information. We show how this redundancy measure can be used within the framework of the Partial Information Decomposition (PID) to give an intuitive decomposition of the multivariate mutual information into redundant, unique and synergistic contributions. We compare our new measure to existing approaches over a range of example systems, including continuous Gaussian variables. Matlab code for the measure is provided, including all considered examples.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ince, Dr Robin
Authors: Ince, R. A.A.
College/School:College of Medical Veterinary and Life Sciences > Institute of Neuroscience and Psychology
Journal Name:Entropy
Publisher:MDPI
ISSN:1099-4300
ISSN (Online):1099-4300
Published Online:29 June 2017
Copyright Holders:Copyright © 2017 The Author
First Published:First published in Entropy 19(7): 318
Publisher Policy:Reproduced under a Creative Commons license

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
698281Brain Algorithmics: Reverse Engineering Dynamic Information Processing Networks from MEG time seriesPhilippe SchynsWellcome Trust (WELLCOTR)107802/Z/15/ZINP - CENTRE FOR COGNITIVE NEUROIMAGING
700661Visual Commonsense for Scene UnderstandingPhilippe SchynsEngineering and Physical Sciences Research Council (EPSRC)EP/N019261/1INP - CENTRE FOR COGNITIVE NEUROIMAGING