Towards Moment-Constrained Causal Modeling
Matteo Guardiani, Philipp G. Frank, Andrija Kostić, Torsten A. Enßlin · 2022
The fundamental problem with causal inference involves discovering causal relations between variables used to describe observational data. We address this problem within the formalism of information field theory (IFT). Specifically, we focus on the problems of bivariate causal discovery (X → Y, Y → X) from an observational dataset (X,Y). The bivariate case is especially interesting because the methods of statistical independence testing are not applicable here. For this class of problems, we propose the moment-constrained causal model (MCM). The MCM goes beyond the additive noise model by exploiting Bayesian hierarchical modeling to provide non-parametric reconstructions of the observational distributions. In order to identify the correct causal direction, we compare the performance of our newly-developed Bayesian inference algorithm for different causal directions (X→Y, Y → X) by calculating the evidence lower bound (ELBO). To this end, we developed a new method for the ELBO estimation that takes advantage of the adopted variational inference scheme for parameter inference.