Math @ Duke

Publications [#264735] of Guillermo Sapiro
Papers Published
 Fiori, M; MusÃ©, P; Sapiro, G, Topology constraints in graphical models,
Advances in Neural Information Processing Systems, vol. 1
(2012),
pp. 791799, ISSN 10495258
(last updated on 2017/12/17)
Abstract: Graphical models are a very useful tool to describe and understand natural phenomena, from gene expression to climate change and social interactions. The topological structure of these graphs/networks is a fundamental part of the analysis, and in many cases the main goal of the study. However, little work has been done on incorporating prior topological knowledge onto the estimation of the underlying graphical models from sample data. In this work we propose extensions to the basic joint regression model for network estimation, which explicitly incorporate graphtopological constraints into the corresponding optimization approach. The first proposed extension includes an eigenvector centrality constraint, thereby promoting this important prior topological property. The second developed extension promotes the formation of certain motifs, triangleshaped ones in particular, which are known to exist for example in genetic regulatory networks. The presentation of the underlying formulations, which serve as examples of the introduction of topological constraints in network estimation, is complemented with examples in diverse datasets demonstrating the importance of incorporating such critical prior knowledge.


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