Approximate Counting of Graphical Models Via MCMC Revisited
arXiv:1301.7189
Abstract
In Peña (2007), MCMC sampling is applied to approximately calculate the ratio of essential graphs (EGs) to directed acyclic graphs (DAGs) for up to 20 nodes. In the present paper, we extend that work from 20 to 31 nodes. We also extend that work by computing the approximate ratio of connected EGs to connected DAGs, of connected EGs to EGs, and of connected DAGs to DAGs. Furthermore, we prove that the latter ratio is asymptotically 1. We also discuss the implications of these results for learning DAGs from data.
In Proceedings of the 15th Conference of the Spanish Association for Artificial Intelligence (CAEPIA 2013). Lecture Notes in Artificial Intelligence