Causality Modeling and Statistical Generative Mechanisms

Abstract

Causality notion lies at the heart of science, but when statistics tries to address this issue some profound questions remain unanswered. How statistical inference in probabilistic terms is linked with causality? What modern causality models offer that is substantially different from the traditional dependency models like regression or decision trees, and if yes, do they deliver these promises? How causality models are related to statistical and machine learning techniques? What is the relationship between causality modeling, statistical inference, and machine learning on one side – and operations research and optimization on the other? Or, more generally: if the causal picture of the world is a commonly accepted goal of any science, could the non-causal statistical models be of any use? If yes – in what sense? If not – why are they so widely used? The insufficient level of detail in discussions of these and similar problems creates a lot of confusion, especially now, when lauded terms like Data Mining, Big Data, Deep Learning and others appear even in the non-professional media. This paper inspects the underlying logic of different approaches, directly or indirectly, related with causality. It shows that even established methods are vulnerable to small deviations from the ideal setting; that the leading approaches to statistical causality, Structural Equations Modeling (SEM), Directed Acyclic Graphs (DAG) and Potential Outcomes (PO) theories do not provide a coherent causality theory, and argues that this theory is impossible on pure statistical grounds. It also discusses a new approach in which the concept of causality is replaced by the concept of dependent variable generation. Separation of the variables generating the outcome from others just correlated with it (which often separates also causal from non-causal variables) is proposed.