Experimental Learning of Causal Models with Latent Variables

This article discusses graphical models that can handle latent variables without explicitly modeling them quantitatively. There exist several paradigms for such problem domains. Two of them are semi-Markovian causal models and maximal ancestral graphs. Applying these techniques to a problem domain consists of several steps, typically: structure learning from observational and experimental data, parameter learning, probabilistic inference, and, quantitative causal inference. A problem is that research in each of the existing approaches only focuses on one or a few of all the steps involved in the process of modeling a problem including latent variables. In other work we have investigated the integral process from observational and experimental data unto different types of efficient inference. The goal of this article is to focus on learning the structure of causal models in the presence of latent variables from a combination of observational and experimental data. Semi-Markovian causal models (SMCMs) are an approach developed by Pearl and Tian [3, 6]. They are specifically suited for performing quantitative causal inference in the presence of latent variables. However, at this time no efficient parametrisation of such models is provided and there are no techniques for performing efficient probabilistic inference. Furthermore there are no techniques to learn these models from data issued from observations, experiments or both. Maximal ancestral graphs (MAGs) are an approach developed by Richardson et al. [4]. They are specifically suited for structure learning in the presence of latent variables from observational data. However, the techniques only learn up to Markov equivalence and provide no clues on which additional experiments to perform in order to obtain the fully oriented causal graph. See [1, 2] for that type of results for Bayesian networks without latent variables. Furthermore, as of yet no parametrisation for discrete variables is provided for MAGs and no techniques for probabilistic inference have been developed. There is some work on algorithms for causal inference, but it is restricted to causal inference