Understanding causation via correlations and linear response theory

TL;DR

This paper demonstrates how time correlations and fluctuation-response theory can be used to infer causal relations in multi-dimensional linear Markov processes, providing a practical approach to understanding causation beyond simple correlation.

Contribution

It introduces a method leveraging fluctuation-response formalism to identify direct causal links and quantify causation in linear Markov systems, even with weak nonlinearities.

Findings

Fluctuation-response formalism reveals direct causal links.

Method provides a causal measure with clear physical interpretation.

Useful proxy for causation in weakly nonlinear systems.

Abstract

In spite of the (correct) common-wisdom statement correlation does not imply causation, a proper employ of time correlations and of fluctuation-response theory allows to understand the causal relations between the variables of a multi-dimensional linear Markov process. It is shown that the fluctuation-response formalism can be used both to find the direct causal links between the variables of a system and to introduce a degree of causation, cumulative in time, whose physical interpretation is straightforward. Although for generic non-linear dynamics there is no simple exact relationship between correlations and response functions, the described protocol can still give a useful proxy also in presence of weak nonlinear terms.