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Functional Network Topology Learning and Sensitivity Analysis Based on ANOVA Decomposition

castie{at}unican.es Department of Applied Mathematics and Computational Sciences, University of Cantabria and University of Castilla–La Mancha, Spain

Noelia Sánchez-Maroño

nsanchez{at}udc.es

Amparo Alonso-Betanzos

ciamparo{at}udc.cs Computer Science Department, University of A Coruña, Spain

Carmen Castillo

MariaCarmen.Castillo{at}uclm.es Department of Civil Engineering, University of Castilla–La Mancha, Spain

A new methodology for learning the topology of a functional network from data, based on the ANOVA decomposition technique, is presented. The method determines sensitivity (importance) indices that allow a decision to be made as to which set of interactions among variables is relevant and which is irrelevant to the problem under study. This immediately suggests the network topology to be used in a given problem. Moreover, local sensitivities to small changes in the data can be easily calculated. In this way, the dual optimization problem gives the local sensitivities. The methods are illustrated by their application to artificial and real examples.