In clique tree clustering, inference consists of propagation in a clique tree compiled from a Bayesian network. In this paper, we develop an analytical approach to characterizing clique tree growth as a function of increasing Bayesian network connectedness, specifically: (i) the expected number of moral edges in their moral graphs or (ii) the ratio of the number of non-root nodes to the number of root nodes. In experiments, we systematically increase the connectivity of bipartite Bayesian networks, and find that clique tree size growth is well-approximated by Gompertz growth curves. This research improves the understanding of the scaling behavior of clique tree clustering, provides a foundation for benchmarking and developing improved BN inference algorithms, and presents an aid for analytical trade-off studies of tree clustering using growth curves.

Reference:

O. J. Mengshoel, "Macroscopic Models of Clique Tree Growth for Bayesian Networks." In Proc. of the 22nd National Conference on Artificial Intelligence (AAAI-07). July 2007, Vancouver, Canada, pp. 1256-1262.

BibTex Reference:

@inproceedings{mengshoel07macroscopic, author = "Mengshoel, O. J.", title = "Macroscopic Models of Clique Tree Growth for {Bayesian} Networks", year = "2007", booktitle = {Proceedings of the Twenty-Second National Conference on Artificial Intelligence (AAAI-07)}, pages = "1256-1262", address = "Vancouver, British Columbia" }