The interventional Bayesian Gaussian equivalent score for Bayesian causal inference with unknown soft interventions

Jack Kuipers, Giusi Moffa

Keywords: Graphical models, Bayesian networks, Directed acyclic graphs, Bayesian scores, Structure learning, Causal inference, Interventional data

TL;DR: We derive a Bayesian score for continuous data with unknown interventions, and showcase its use in simulations and on real data

Abstract: Describing the causal relations governing a system is a fundamental task in many scientific fields, ideally addressed by experimental studies. However, obtaining data under intervention scenarios may not always be feasible, while discovering causal relations from purely observational data is notoriously challenging. In certain settings, such as genomics, we may have data from heterogeneous study conditions, with soft (partial) interventions only pertaining to a subset of the study variables, whose effects and targets are possibly unknown. Combining data from experimental and observational studies offers the opportunity to leverage both domains and improve the identifiability of causal structures. To this end, we define the interventional BGe score for a mixture of observational and interventional data for linear-Gaussian models, where the targets and effects of intervention may be unknown. Prerogative of our method is that it takes a Bayesian perspective leading to a full characterisation of the posterior distribution of the DAG structures. Given a sample of DAGs, one can also automatically derive full posterior distributions of the intervention effects. Consequently, the method effectively captures the uncertainty both in the structure and the parameter estimates. We additionally demonstrate the performance of the approach both in simulations and data analysis applications. Codes to reproduce the simulations and analyses are publicly available at https://github.com/jackkuipers/iBGe.

Submission Number: 51