L Costa, JQ Smith, TE Nichols and J Cussens
Searching Multiregression Dynamic Models of Resting-Stat fMRI Networks using Integer Programming
Abstract: A Multiregression Dynamic Model (MDM) is a class of multivariate time series that represents various dynamic causal processes in a graphical way. One of the advantages of this class is that, in contrast to many other Dynamic Bayesian Networks, the hypothesized relationships accommodate conditional conjugate inference. We demonstrate for the first time how it is straightforward to search over all possible connectivity networks with dynamically changing intensity of transmission to find the MAP model within this class. This search method is made feasible by using a novel application of an Integer Programming algorithm. We then develop methods customised to networks based on resting-state Functional Magnetic Resonance Imaging (fMRI) data. We demonstrate the efficacy of our dynamic models within this domain and, in particular, computationally efficient search of 11-node DAG model space. We illustrate how diagnostic methods, analogous to those defined for static Bayesian Networks, can be used to suggest embellishment of the model class to extend the process of model selection. All methods are illustrated using simulated and real resting fMRI data.
Keywords: Multiregression Dynamic Model, Bayesian Network, Integer Program Algorithm, Model Selection, Functional magnetic resonance imaging (fMRI).