Combined cause inference: Definition, model and performance

Abstract In recent years, many methods have been developed for discovering causal relationships from observed data. However, as an important kind of causes existing in many causal systems, combined causes (e.g. multi-factor causes consisting of two or more component variables that individually might not be a cause) have not received enough attention. The existing approach includes both individual and combined variables in the causal discovery process using constraint-based methods, can neither distinguish a set of Markov equivalence classes nor identify a combined cause containing one (or more) individual cause(s), therefore can output only some combined causes, instead of all combined causes. In this paper, we first subsume all possible combined causes into three types and give them formal definitions, then extend the additive noise model (ANM) to infer combined causes. We show that if a candidate variable set X w.r.t. a target Y satisfies: (1) allowing ANM for only the forward direction X → Y , and (2) no disturbance variable is contained in X, i.e., removing any component of X will weaken the causal relationship between X and Y, then X forms a combined cause. Based on this finding, we develop an efficient method to discover combined causes. Furthermore, we also conduct extensive experiments to validate the proposed method on both synthetic and real-world data sets.