Understanding causation via correlations and linear response theory

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.

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• The Many Faces of Fluctuation-Dissipation Relations Out of Equilibrium
• Assessing transfer entropy from biochemical data
• A handy fluctuation-dissipation relation to approach generic noisy systems and chaotic dynamics
• The interplay between diversity and noise in an excitable cell network model
• Predictors and Predictands of Linear Response in Spatially Extended Systems
• Prediction and Inference: From Models and Data to Artificial Intelligence
• Fluctuation-response theorem for Kullback-Leibler divergences to quantify causation
• Koopman operator-based discussion on partial observation in stochastic systems