Causal Discovery using Bayesian Model Selection
Anish Dhir Mark van der Wilk
With only observational data on two variables, and without other assumptions,
it is not possible to infer which one causes the other. Much of the causal
literature has focused on guaranteeing identifiability of causal direction in
statistical models for datasets where strong assumptions hold, such as additive
noise or restrictions on parameter count. These methods are then subsequently
tested on realistic datasets, most of which violate their assumptions. Building
on previous attempts, we show how to use causal assumptions within the Bayesian
framework. This allows us to specify models with realistic assumptions, while
also encoding independent causal mechanisms, leading to an asymmetry between
the causal directions. Identifying causal direction then becomes a Bayesian
model selection problem. We analyse why Bayesian model selection works for
known identifiable cases and flexible model classes, while also providing
correctness guarantees about its behaviour. To demonstrate our approach, we
construct a Bayesian non-parametric model that can flexibly model the joint. We
then outperform previous methods on a wide range of benchmark datasets with
varying data generating assumptions showing the usefulness of our method.