Building causation links in stochastic nonlinear systems from data

Causal relationships play a fundamental role in understanding the world around us. The ability to identify and understand cause-and-effect relationships is critical to making informed decisions, predicting outcomes, and developing effective strategies. However, deciphering causal relationships from observational data is a difficult task, as correlations alone may not provide definitive evidence of causality. In recent years, the field of machine learning (ML) has emerged as a powerful tool, offering new opportunities for uncovering hidden causal mechanisms and better understanding complex systems. In this work, we address the issue of detecting the intrinsic causal links of a large class of complex systems in the framework of the response theory in physics. We develop some theoretical ideas put forward by Aurell and Del Farraro [J. Phys. Conf. Ser. 699, 012002 (2016)10.1088/1742-6596/699/1/012002], and technically we use state-of-the-art ML techniques to build up models from data. We consider both linear stochastic and nonlinear systems. Finally, we compute the asymptotic efficiency of the linear-response-based causal predictor in a case of a large-scale Markov process network of linear interactions.