Optimal experimental design via Bayesian optimization: active causal structure learning for Gaussian process networks
This work addresses causal structure learning for researchers in fields like biology or economics where continuous, non-linear data is common, representing an incremental advance by extending Bayesian active learning to this specific setting.
The paper tackles the problem of causal discovery through targeted interventions in continuous random variables with non-linear relationships, using Gaussian process priors, and proposes a Bayesian optimization approach to efficiently select maximally informative experiments, achieving computational efficiency in handling uncountable intervention sets.
We study the problem of causal discovery through targeted interventions. Starting from few observational measurements, we follow a Bayesian active learning approach to perform those experiments which, in expectation with respect to the current model, are maximally informative about the underlying causal structure. Unlike previous work, we consider the setting of continuous random variables with non-linear functional relationships, modelled with Gaussian process priors. To address the arising problem of choosing from an uncountable set of possible interventions, we propose to use Bayesian optimisation to efficiently maximise a Monte Carlo estimate of the expected information gain.