The Bayesian approach to structure learning in Bayesian networks aims at summarizing the posterior distribution of the network structure, that is, a directed acyclig graph (DAG). Natural formulations of the problem are computationally hard, and can be currently solved exactly only when the network has at most about 30 nodes. For larger networks, the state-of-the-art methods are based on the Markov chain Monte Carlo method (MCMC).  In particular, two recent articles present two MCMC methods that are based on quite different ideas:

1. Teppo Niinimäki, Pekka Parviainen, Mikko Koivisto: Structure discovery in Bayesian networks by sampling partial orders. Journal of Machine Learning Research,17(57):1−47, 2016.

2. Robert J. B. Goudie, Sach Mukherjee: A Gibbs sampler for learning DAGs. Journal of Machine Learning Research, 17(30):1−39, 2016.

Which of these two methods is more efficient? This is currently an open question. The task of the Master's thesis is to experimentally compare these methods using available implementations.