Many questions in science, policy making and everyday life are of a causal nature: how would changing A influence B? Causal inference, a branch of statistics and machine learning, studies how cause-effect relationships can be discovered from data and how these can be used for making predictions in situations where a system has been perturbed by an external intervention. The ability to reliably make such causal predictions is of great value for practical applications in a variety of disciplines. Over the last two decades, remarkable progress has been made in the field. However, even though state-of-the-art causal inference algorithms work well on simulated data when all their assumptions are met, there is still a considerable gap between theory and practice. The goal of CAFES was to bridge that gap by developing theory and algorithms that would enable large-scale applications of causal inference in various challenging domains in science, industry and decision making.
The key challenge that was addressed is how to deal with cyclic causal relationships (“feedback loops”). Feedback loops are very common in many domains (e.g. biology, economy and climatology), but have mostly been ignored so far in the field. Building on recently established connections between dynamical systems and causal models, CAFES has developed new mathematical representations of causality and conditional independence properties of feedback systems. Theory has been developed that concerns properties of these mathematical models of cyclic casuality. Based on this theory, algorithms have been designed to discover causal relations from data and to predict the consequences of interventions on systems. While the focus has been on modeling static causality of systems at equilibrium, extensions of the theory and algorithms for dynamical systems have been proposed as well. In order to optimally use available resources, computationally efficient algorithms for causal inference from observational and interventional data in the context of confounders and feedback have been developed. These algorithms have been applied on several use cases in molecular biology, one of the most promising areas for automated causal inference from data. While we have made significant conceptual progress and the research has greatly advanced our understanding of cyclic causality, we conclude that more research is necessary to enable practical applications.
