Bayesian structure learning in graphical models
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
This thesis consists of two papers studying structure learning in probabilistic graphical models for both undirected graphs anddirected acyclic graphs (DAGs).
Paper A, presents a novel family of graph theoretical algorithms, called the junction tree expanders, that incrementally construct junction trees for decomposable graphs. Due to its Markovian property, the junction tree expanders are shown to be suitable for proposal kernels in a sequential Monte Carlo (SMC) sampling scheme for approximating a graph posterior distribution. A simulation study is performed for the case of Gaussian decomposable graphical models showing efficiency of the suggested unified approach for both structural and parametric Bayesian inference.
Paper B, develops a novel prior distribution over DAGs with the ability to express prior knowledge in terms of graph layerings. In conjunction with the prior, a search and score algorithm based on the layering property of DAGs, is developed for performing structure learning in Bayesian networks. A simulation study shows that the search and score algorithm along with the prior has superior performance for learning graph with a clearly layered structure compared with other priors.
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. , viii, 19 p.
Bayesian statistics, graphical models, Bayesian networks, Markov networks, structure learning
Probability Theory and Statistics
Research subject Applied and Computational Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-179852ISBN: 978-91-7595-832-3OAI: oai:DiVA.org:kth-179852DiVA: diva2:892063
2016-01-28, Rum 3418, Instititionen för matematik, Lindstedtsvägen 25, Kungliga Tekniska Högskolan, Stockholm, 14:00 (English)
Markström, Klas, Associate Professor
Pavlenko, Tatjana, Associate Professor
QC 201601112016-01-112016-01-042016-01-11Bibliographically approved
List of papers