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Factorial graphical models for dynamic networks

Published online by Cambridge University Press:  12 February 2015

ERNST WIT  and
ANTONINO ABBRUZZO
ERNST WIT
Affiliation:
Johann Bernoulli Institute, University of Groningen, 9747 AG Groningen, the Netherlands (e-mail: e.c.wit@rug.nl)
ANTONINO ABBRUZZO
Affiliation:
Dipartimento Scienze Economiche, Aziendali e Statistiche, University of Palermo, 90128 Palermo, Italy
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Abstract

Dynamic network models describe many important scientific processes, from cell biology and epidemiology to sociology and finance. Estimating dynamic networks from noisy time series data is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is typically larger than the number of observations. However, a characteristic of many real life networks is that they are sparse. For example, the molecular structure of genes make interactions with other components a highly-structured and, therefore, a sparse process. Until now, the literature has focused on static networks, which lack specific temporal interpretations.

We propose a flexible collection of ANOVA-like dynamic network models, where the user can select specific time dynamics, known presence or absence of links, and a particular autoregressive structure. We use undirected graphical models with block equality constraints on the parameters. This reduces the number of parameters, increases the accuracy of the estimates and makes interpretation of the results more relevant. We illustrate the flexibility of the method on both synthetic and real data.

Keywords

constrained optimizationdynamic networksGaussian graphical modelspenalized likelihoodtime-course datagene networks
Type
Research Article
Information
Network Science , Volume 3 , Issue 1: Networks in Space and in Time: Methods and Applications , March 2015 , pp. 37 - 57
Copyright
Copyright © Cambridge University Press 2015 

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