Determining Network Structure from Data: Nonlinear Modeling Methods

In this entry we focus on inference of network structures from data. One possible approach to studying networks is to model the nodes, such as neurons, and generate networks and run simulations and observe the network behavior. This approach requires on a priori assumptions about the constituent parts; for instance, Hodgkin-Huxley neurons may be coupled and the resulting network behavior is investigated. The model behaviors can be compared to the measured neuronal signals through statistical analysis. However, this approach only provides indirect information about the network structure. An alternative approach to studying network structure is to use parametric, semiparametric, and nonparametric analyses of the observed signals and reconstruct the network connections. Such analyses are essential tools for systems in which network structure is not known, such as when anatomical connections are not known or information is not sufficient.

A particular challenge when inferring the network structure from data lies in the fact that analysis techniques to investigate interactions are often bivariate, investigating pairwise connections. Often, analyses cannot distinguish between direct and indirect interactions. A good measure of coupling between nodes should be able to distinguish direct and indirect interactions. To achieve this, a multivariate data analysis approach needs to be used. For linear systems multivariate data analysis approaches have been developed over the past decades. However, for nonlinear systems, the development of multivariate analysis techniques is in its infancy. Nonlinear approaches typically require computationally intensive algorithms and large data sets which have limited their application.

In this entry, we provide a survey of approaches for inferring the network structure from nonlinear systems using nonlinear data-based modeling.