A Combinatorial Approach to Causal Inference
Thomas C. Fraser · arXiv (Cornell University) · 2019
The objective of causal inference is to learn the network of causal relationships holding between a system of variables from the correlations that these variables exhibit; a sub-problem of which is to certify whether or not a given causal hypothesis is compatible with the observed correlations. A particularly challenging setting for causal inference is in the presence of partial information; i.e. when some of the variables are hidden/latent. In this present work, we introduce the possible worlds framework as a method for deciding causal compatibility in this difficult setting. We define a graphical object called an possible worlds diagram, which compactly depicts the set of all possible observations. From this construction, we demonstrate explicitly, using several examples, how to prove causal incompatibility. In fact, we use these constructions to prove causal incompatibility where no other techniques have been able to. Moreover, we prove that the possible worlds framework can be adapted to provide a complete solution to the possibilistic causal compatibility problem. Even more, we also discuss how to exploit graphical symmetries and cross-world consistency constraints in order to implement a hierarchy of necessary compatibility tests that we prove converges to sufficiency.