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Lizier, Joseph T

Rubinov, Mikail

BMC Neuroscience

PubMed

Joseph T Lizier

Mikail Rubinov

Springer - Publisher Connector

Inferring effective computational connectivity using incrementally conditioned multivariate transfer entropy

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Apollo (Cambridge)

POSTER PRESENTATION Open AccessInferring effective computational connectivityusing incrementally conditioned multivariatetransfer entropyJoseph T Lizier1,2*, Mikail Rubinov3,4From Twenty Second Annual Computational Neuroscience Meeting: CNS*2013Paris, France. 13-18 July 2013Effective connectivity analysis is a popular approach incomputational neuroscience, whereby one seeks to infera network of directed edges between neural variables (e.g.voxels or regions in fMRI, or reconstructed source timeseries in MEG data) which can explain their observedtime-series dynamics. This is an important approach inunderstanding brain function, contrasting with functionalconnectivity analysis in being directed and dynamic, andwith structural connectivity analysis in not requiringinterventions and in being task-modulated. In particular,effective connectivity analysis seeks to find a minimal cir-cuit model that can reconstruct the activity patterns con-tained in the given data. Ideally, such inference would be:made using model-free techniques; capture non-linear,multivariate, directional relationships; handle smallamounts of data, and be statistically robust.The information-theoretic measure transfer entropy(TE) [1] (a non-linear Granger causality) is becoming* Correspondence: joseph.lizier@csiro.au1CSIRO Information and Communications Technology Centre, Marsfield, NSW2122, AustraliaFull list of author information is available at the end of the articleFigure 1 ROC curve for inference on discrete-time autoregressive time-series for 400 observations (100 nodes, 400 edges, randomdirected structure, edge weights 0.5, random noise variance 1).Lizier and Rubinov BMC Neuroscience 2013, 14(Suppl 1):P337http://www.biomedcentral.com/1471-2202/14/S1/P337© 2013 Lizier and Rubinov; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the CreativeCommons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.widely used for this purpose [2]. However its use is gen-erally focussed only on interactions between a singlesource and destination (inferring an edge where TE isstatistically significant), or else attempting multivariateconsiderations by conditioning on all other variables inthe system (only practically possible with small numbersof variables or linear interactions). We aim to extendTE-based effective network inference to multivariatetechniques, specifically: capturing collective interactionswhere target outcomes are due to multiple source vari-ables (synergies); eliminating spurious connections forcorrelated sources (redundancies); and avoiding combi-natorial explosions in source groups evaluated. We aimto maximize inference of true interactions while mini-mizing inference of spurious interactions.In this manner, we describe a new method [3] whichaddresses the above requirements in considering multi-variate source interactions. For each node in the network,the method identifies the set of source nodes which pro-vide the most statistically significant information regard-ing its dynamics, and are thus inferred as those sourceinformation nodes from which that destination is com-puted. This is done using incrementally conditioned TE,gradually building the set of source nodes for a destina-tion conditioned on the previously identified sources.For validation purposes, we apply our method to varioussynthetic models of dynamics on networks (e.g. linearlycoupled Gaussian autoregressive time series in Figure 1),and demonstrate the utility of the method in revealing sig-nificant proportions of the underlying structural networkgiven only short time-series of the network dynamics. Theresults show particular utility in comparison to othermethods (i.e. Figure 1 shows our incremental method sig-nificantly outperforms conditioning on all other variables,even on this data set with linear relationships where thelatter is possible). Following validation studies we willapply our technique to neuroimaging data sets.Author details1CSIRO Information and Communications Technology Centre, Marsfield, NSW2122, Australia. 2Max Planck Institute for Mathematics in the Sciences, 04103Leipzig, Germany. 3Department of Psychiatry, University of Cambridge,Cambridge, UK. 4Churchill College, University of Cambridge, Cambridge, UK.Published: 8 July 2013References1. Schreiber T: Measuring information transfer. Phys Rev Lett 2000,85:461-464.2. Vicente R, Wibral M, Lindner M, Pipa G: Transfer entropy-a model-freemeasure of effective connectivity for the neurosciences. J Comp Neurosci2011, 30(1):45-67.3. Lizier JT, Rubinov M: Multivariate construction of effective computationalnetworks from observational data. Max Planck Institute for Mathematics inthe Sciences Preprint 25/2012 2012.doi:10.1186/1471-2202-14-S1-P337Cite this article as: Lizier and Rubinov: Inferring effective computationalconnectivity using incrementally conditioned multivariate transferentropy. BMC Neuroscience 2013 14(Suppl 1):P337.Submit your next manuscript to BioMed Centraland take full advantage of: • Convenient online submission• Thorough peer review• No space constraints or color figure charges• Immediate publication on acceptance• Inclusion in PubMed, CAS, Scopus and Google Scholar• Research which is freely available for redistributionSubmit your manuscript at www.biomedcentral.com/submitLizier and Rubinov BMC Neuroscience 2013, 14(Suppl 1):P337http://www.biomedcentral.com/1471-2202/14/S1/P337Page 2 of 2

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Inferring effective computational connectivity using incrementally conditioned multivariate transfer entropy

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