Learning Semi-Markovian Causal Models using Experiments

Semi-Markovian causal models (SMCMs) are an extension of causal Bayesian networks for modeling problems with latent variables. However, there is a big gap between the SMCMs used in theoretical studies and the models that can be learned from observational data alone. The result of standard algorithms for learning from observations, is a complete partially ancestral graph (CPAG), representing the Markov equivalence class of maximal ancestral graphs (MAGs). In MAGs not all edges can be interpreted as immediate causal relationships. In order to apply state-of-the-art causal inference techniques we need to completely orient the learned CPAG and to transform the result into a SMCM by removing non-causal edges. In this paper we combine recent work on MAG structure learning from observational data with causal learning from experiments in order to achieve that goal. More specifically, we provide a set of rules that indicate which experiments are needed in order to transform a CPAG to a completely oriented SMCM and how the results of these experiments have to be processed. We will propose an alternative representation for SMCMs that can easily be parametrised and where the parameters can be learned with classical methods. Finally, we show how this parametrisation can be used to develop methods to efficiently perform both probabilistic and causal inference.