Markov Abstraction Equivalence Classes

Abstract

The last decade, the influence and the use of causal models is growing in several scientific disciplines. Recently, Beckers & Halpern (2019) and Beckers, Eberhardt & Halpern (2019) developed an account of abstraction for causal models which makes it possible to go from a low-level causal model to a high-level causal model, including interventions on the low-level and high-level causal model. This thesis combines the theory of abstracting causal models with the theory of Markov Equivalence Classes to come to an account of Markov Abstraction Equivalence Classes. A Markov Abstraction Equivalence Class is a subset of a Markov Equivalence Class, generated by using the information of an abstraction to eliminate models from the Markov Equivalence Class. Markov Abstraction Equivalence Classes reduce the search space of causal search algorithms, which improves the performance of causal search algorithms. The pcabs algorithm is developed to put the theory of Markov Abstraction Equivalence Classes into practice. This thesis builds on the theory of causal models, causal search algorithms, Markov Equivalence Classes and constructive tau-abstraction.