Large-Scale Kernelized Granger Causality (lsKGC) for Inferring Topology of Directed Graphs in Brain Networks

Graph topology inference in networks with co-evolving and interacting time-series is crucial for network studies. Vector autoregressive models (VAR) are popular approaches for topology inference of directed graphs; however, topology estimation becomes ill-posed in large networks with short time series. The present paper proposes a novel topology inference method for analyzing directed networks with co-evolving nodal processes that solves the ill-posedness problem. The proposed method, large-scale kernelized Granger causality (lsKGC), uses kernel functions to transform data into a low-dimensional feature space, solves the autoregressive problem in the feature space, and then finds the pre-images in the input space to infer the topology. Extensive simulations on synthetic datasets with nonlinear and linear dependencies and known ground-truth demonstrate significant improvement in the Area Under the receiver operating characteristic Curve (AUC) for network recovery compared to existing methods. Furthermore, tests on synthetic semi-realistic datasets from functional magnetic resonance imaging (fMRI) demonstrate significant improvement in the AUC for topology inference, enhancing the prior results of the best competing methods by 15.4 percent, which confirms the benefits of the proposed method as compared to existing literature.