Structural equation models (SEMs) and vector autoregressive models (VARMs)
are two broad families of approaches that have been shown useful in effective
brain connectivity studies. While VARMs postulate that a given region of
interest in the brain is directionally connected to another one by virtue of
time-lagged influences, SEMs assert that causal dependencies arise due to
contemporaneous effects, and may even be adopted when nodal measurements are
not necessarily multivariate time series. To unify these complementary
perspectives, linear structural vector autoregressive models (SVARMs) that
leverage both contemporaneous and time-lagged nodal data have recently been put
forth. Albeit simple and tractable, linear SVARMs are quite limited since they
are incapable of modeling nonlinear dependencies between neuronal time series.
To this end, the overarching goal of the present paper is to considerably
broaden the span of linear SVARMs by capturing nonlinearities through kernels,
which have recently emerged as a powerful nonlinear modeling framework in
canonical machine learning tasks, e.g., regression, classification, and
dimensionality reduction. The merits of kernel-based methods are extended here
to the task of learning the effective brain connectivity, and an efficient
regularized estimator is put forth to leverage the edge sparsity inherent to
real-world complex networks. Judicious kernel choice from a preselected
dictionary of kernels is also addressed using a data-driven approach. Extensive
numerical tests on ECoG data captured through a study on epileptic seizures
demonstrate that it is possible to unveil previously unknown causal links
between brain regions of interest.

通过利用核函数来捕捉非线性因素，文章旨在通过构建线性结构向量自回归模型来扩展大脑连接研究的范围，并提供一种有效的正则化估计方法，以揭示感兴趣的大脑区域之间的先前未知的因果联系。