The Minimal Hoppe-Beta Prior Distribution for Directed Acyclic Graphs and Structure Learning
(English)Manuscript (preprint) (Other academic)
The main contribution of this article is a new prior distribution over directed acyclic graphs intended for structured Bayesian networks, where the structure is given by an ordered block model. That is, the nodes of the graph are objects which fall into categories or blocks; the blocks have a natural ordering or ranking. The presence of a relationship between two objects is denoted by a directed edge, from the object of category of lower rank to the object of higher rank. The models considered here were introduced in Kemp et al.  for relational data and extended to multivariate data in Mansinghka et al. .
We consider the situation where the nodes of the graph represent random variables, whose joint probability distribution factorises along the DAG. We use a minimal layering of the DAG to express the prior. We describe Monte Carlo schemes, with a similar generative that was used for prior, for finding the optimal a posteriori structure given a data matrix and compare the performance with Mansinghka et al. and also with the uniform prior.
Graphical models, Bayesian networks, structure learning, DAG prior
Probability Theory and Statistics
Research subject Applied and Computational Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-180327OAI: oai:DiVA.org:kth-180327DiVA: diva2:892655
QC 201605242016-01-112016-01-112016-05-24Bibliographically approved