Bayesian Causal Inference with Gaussian Process Networks

TL;DR

This work tackles the problem of estimating intervention distributions from observational data using Gaussian Process Networks (GPNs), a flexible nonparametric causal framework. It develops two Bayesian inference pathways: a global Monte Carlo propagation through a known DAG and an efficient local additive-GP approximation, with graph uncertainty incorporated via MCMC over DAGs and importance weighting. The local approach leverages an additive GP model Y = f(X) + sum_{Z∈Pa_X} g_Z(Z) + ε to approximate interventions via backdoor adjustment, offering substantial speedups at the cost of potential misspecification for long causal paths. Empirical results on synthetic data and Arabidopsis gene-expression data show GPNs can identify non-linear, non-Gaussian causal effects and provide calibrated uncertainty, outperforming linear Gaussian baselines in capturing complex dependencies.

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.

Figures (13)

• Figure 1: The DAG used to generate the data for figures \ref{['fig:glob_dag']}-\ref{['fig:loc_nodag']}.
• Figure 2: Estimated intervention expectations derived according to algorithm 1, with a known DAG. Samples are shown in gray, the dashed red line indicates the mean estimate, the green line shows the true data-generating value, and the red area shows an $80\%$ credible interval.
• Figure 3: Estimated intervention expectations derived according to algorithm 2, without a known DAG. Samples are shown in gray, the dashed red line indicates the mean estimate, the green line shows the true data-generating value, and the red area shows an $80\%$ credible interval.
• Figure 4: Estimated intervention expectations derived according to the local approximation with a known DAG. Samples are shown in gray, the dashed red line indicates the mean estimate, the green line shows the true data-generating value, and the red area shows an $80\%$ credible interval.
• Figure 5: Estimated intervention expectations derived according to algorithm 3 without a known DAG. Samples are shown in gray, the dashed red line indicates the mean estimate, the green line shows the true data-generating value, and the red area shows an $80\%$ credible interval.