Fourier Bayesian networks: A novel approach for network structure inference with application to brain connectivity studies from magnetoencephalographic recordings

This thesis proposes a novel approach for connectivity studies in Electrophysiology and Neuroimaging based on Bayesian Network (BN) analysis in the Fourier domain that is named Fourier Bayesian Networks (FBNs). FBNs use the complex information available in time series to make inferences about an unknown network structure. Using the Fourier transform, the frequency power and frequency phase information are estimated; then probabilistic models using power and phase are built and used in the network structure searching algorithm.

FBNs are able to deal with massive datasets with long time series and large numbers of sources. This property is inherited by the Fourier transform from which the Fourier coefficients instead of raw time series are used during network searching.

The analysis of the phase using the Fourier transform makes FBNs non-parametric, meaning that these networks do not rely on a model to make inferences. This is an important property for causality inference since several network unfoldings, as in the case of Dynamic BNs, are not needed. This makes FBNs robust to the underlying model.

The proposed method is tested using multivariate autoregressive (MVAR) and non-linear (NL) systems with the variable model order d. Networks are estimated from the MVAR(d) and NL(d) systems directly and also from a magnetoencephalographic (MEG)-simulated environment where beamforming is implemented for source inference. For all experiments d=1 and d=2 are used. The optimization method for network structure searching is simulated annealing.