A Differential Measure of the Strength of Causation

The ability to quantify the strength of an interaction between events represented by random variables is important in many applications such as medicine and environmental science. We present the problem of measuring the strength of a causal interaction, starting from the linear perspective and generalizing to a nonlinear measure of causal influence, using a differential calculus approach. The proposed measure of causal strength is interpretable and may be estimated efficiently using Gaussian process regression. We validate our estimation approach on several synthesized data sets, considering both static variables and time series.