Algorithms for Causal Discovery on Colored Gaussian DAGs

Sammanfattning

Algorithms for causal discovery are of great interest to modern scientists, with applications in economics, physics, and artificial intelligence. One of the leading causal discovery algorithms is Greedy Equivalence Search (GES). GES is valued for its convergence guarantees, however, under its standard assumptions, it still exhibits uncertainty in the cause-and-effect relationships that it identifies. This thesis examines whether recent theoretical advances by Wu and Drton as well as Boege, Kubjas, Misra, and Solus can be leveraged to develop improved causal discovery algorithms. This work focuses on partially homoscedastic DAG models and compatibly colored DAG models. For both of these, a Markov chain Monte Carlo (MCMC) algorithm and a greedy algorithm for finding causal structures given observed data were developed. The results show that the algorithms provide more accurate causal relationships than GES across a wide range of settings. These findings suggest further research in the field and the development of more advanced algorithms leveraging the new theory.