Bayesian Causal Inference with Gaussian Process Networks

TL;DR

This paper introduces a Bayesian approach for causal inference using Gaussian Process Networks, enabling flexible, nonparametric modeling of causal effects and incorporating uncertainty in causal structure, demonstrated through simulations and gene expression data.

Contribution

It develops a Bayesian framework for causal inference with Gaussian Process Networks, including computational approximations and structure uncertainty integration, advancing nonparametric causal analysis.

Findings

Accurately estimates causal effects in non-Gaussian, non-linear data.

Reflects posterior uncertainty in causal estimates.

Performs well on simulated and real gene expression data.

Abstract

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.