Abstract

The study of causality has drawn the attention of researchers from many different fields for centuries. In particular, nowadays causal inference is a central question in neuroscience and an entire body of research, called brain effective connectivity, is devoted to detecting causal interactions between distinct brain areas. Brain effective connectivity is typically studied by the statistical analysis of direct measurements of the neural activity. The main purpose of this work is on methods for studying time series causality. More in details, we focus on a well-establish criterion of causality: the Granger criterion, which is based on the concepts of temporal precedence and predictability. Firstly, we consider the standard parametric implementation of the Granger criterion that is based on the multivariate autoregressive model, where we face the problem of model identification. For this purpose, we present a new Bayesian method for linear model identification and we explore its capability of modeling the sparsity structure of the signals. As a second contribution, we look at the causal inference through the lens of machine learning and we propose an approach based on the concept of learning from examples. Thus, given a set of signals, their causal interactions are estimated by a classifier that is trained on a synthetic dataset generated by a parametric model. This approach, that we call supervised parametric approach, is implemented by adopting the Granger criterion of causality and compared with the standard parametric measure of Granger causality. Moreover, the roles of the feature space and the generative model of the training set are investigated through a simulation study. Additionally, we show an example of application on rat neural recordings. Finally, we focus on the bias introduced by parametric methods when applied in a real context, i.e. the inability of having a fully realistic generative model. For this purpose, we analyze how the supervised parametric approach can help in making the inference more application-dependent, by exploiting a physiologically plausible generative model.