Telling Cause from Effect using MDL-based Local and Global Regression

Telling cause from effect from observational data is one of the fundamental problems in science [26], [18]. We consider the problem of inferring the most likely direction between two univariate numeric random variables X and Y. That is, we are interested in identifying whether X causes Y, whether Y causes X, or whether they are merely correlated. Traditional methods, that rely on conditional independence tests, cannot decide between the Markov equivalent classes of X Y and Y X [18]. Recently, it has been postulated however that if X Y, there exists an independence between the marginal distribution of the cause, P (X), and the conditional distribution of the effect given the cause, P (Y X) [25], [9]. The state of the art exploits this asymmetry in various ways, and overall obtain up to 70% accuracy on a well-known benchmark of cause-effect pairs [24], [8], [20], [10], [17]. In this paper we break this barrier, and give an elegant score that is computable in linear-time and obtains over 82% accuracy on the same benchmark.