Bayesian Causal Inference with Gaussian Process Networks

Quantifying the causal relationships from purely observational data between variables in a system is a problem that has attracted great attention in the fields of statistics and machine learning. Full knowledge of the causal relations allows predicting the outcome of direct manipulations on the system, which can generally only be known from interventional data obtained by performing experiments such as randomized controlled trials (Eberhardt and Scheines, 2007). Predicting the effect of such manipulations without the need of costly or infeasible experiments is of great practical relevance, specifically in the fields of computational biology (Sachs et al., 2005), medicine (Richens et al., 2020) or AI (Schölkopf, 2022), since a central question concerns how a complex system will react to some treatment or outside influence of the user. Pearl's rules of do-calculus (Pearl, 2000) allow computing the intervention distributions resulting from these external manipulations from the joint distribution of the set of random variables together with a Directed Acyclic Graph (DAG). The DAG represents the qualitative causal relationships among the variables; each node in the graph represents a variable and a directed edge indicates a direct causal effect. Probabilistic models that are based on such DAGs, commonly called causal Bayesian Networks (BNs), provide conventional grounds for probabilistic causal inference, due to their compact representation of the joint distribution and their intuitive graphical description of the causal structure.