Active Bayesian Causal Inference

Causal discovery and causal reasoning are classically treated as separate and consecutive tasks: one first infers the causal graph, and then uses it to estimate causal effects of interventions. However, such a two-stage approach is uneconomical, especially in terms of actively collected interventional data, since the causal query of interest may not require a fully-specified causal model. From a Bayesian perspective, it is also unnatural, since a causal query (e.g., the causal graph or some causal effect) can be viewed as a latent quantity subject to posterior inference—quantities that are not of direct interest ought to be marginalized out in this process, thus contributing to our overall uncertainty. In this work, we propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active learning framework for integrated causal discovery and reasoning, i.e., for jointly inferring a posterior over causal models and queries of interest. In our approach to ABCI, we focus on the class of causally-sufficient nonlinear additive Gaussian noise models, which we model using Gaussian processes. To capture the space of causal graphs, we use a continuous latent graph representation, allowing our approach to scale to practically relevant problem sizes. We sequentially design experiments that are maximally informative about our target causal query, collect the corresponding interventional data, update our beliefs, and repeat. Through simulations, we demonstrate that our approach is more data-efficient than existing methods that only focus on learning the full causal graph. This allows us to accurately learn downstream causal queries from fewer samples, while providing well-calibrated uncertainty estimates of the quantities of interest.