Bayesian Causal Inference with Gaussian Process Networks
Enrico Giudice Jack Kuipers Giusi Moffa
Causal discovery and inference from observational data is an essential
problem in statistics posing both modeling and computational challenges. These
are typically addressed by imposing strict assumptions on the joint
distribution such as linearity. We consider the problem of the Bayesian
estimation of the effects of hypothetical interventions in the Gaussian Process
Network (GPN) model, a flexible causal framework which allows describing the
causal relationships nonparametrically. We detail how to perform causal
inference on GPNs by simulating the effect of an intervention across the whole
network and propagating the effect of the intervention on downstream variables.
We further derive a simpler computational approximation by estimating the
intervention distribution as a function of local variables only, modeling the
conditional distributions via additive Gaussian processes. We extend both
frameworks beyond the case of a known causal graph, incorporating uncertainty
about the causal structure via Markov chain Monte Carlo methods. Simulation
studies show that our approach is able to identify the effects of hypothetical
interventions with non-Gaussian, non-linear observational data and accurately
reflect the posterior uncertainty of the causal estimates. Finally we compare
the results of our GPN-based causal inference approach to existing methods on a
dataset of $A.~thaliana$ gene expressions.