Causal network reconstruction from nonlinear time series: A comparative study

Reconstructing causal networks from observed time series is a common problem in diverse science and engineering fields, and the challenge can increase with network size. Unfortunately, systematic comparisons of causal inference techniques have tended to concentrate on small motifs rather than graphs which it would be natural to label as complex networks. In this paper, six widely used methods of causal network reconstruction are systematically benchmarked and contrasted using neuronal models coupled on networks of varied size. Our purpose is concisely to review and explain the basic problems of causality detection using time series, and to compare the performance of varied and practical methods under the extremely relevant, but relatively neglected, conditions of highly nonlinear dynamical systems coupled via networks of many nodes. We find that convergent cross mapping consistently provides the highest precision, but transfer entropy can be preferable when high recall is important. The advantages of convergent cross mapping and transfer entropy over other methods can increase with network size.