Treedy: A Heuristic for Counting and Sampling Subsets
Teppo Niinimaki, Mikko Koivisto
Consider a collection of weighted subsets of a ground set N. Given a query subset Q of N, how fast can one (1) find the weighted sum over all subsets of Q, and (2) sample a subset of Q proportionally to the weights? We present a tree-based greedy heuristic, Treedy, that for a given positive tolerance d answers such counting and sampling queries to within a guaranteed relative error d and total variation distance d, respectively. Experimental results on artificial instances and in application to Bayesian structure discovery in Bayesian networks show that approximations yield dramatic savings in running time compared to exact computation, and that Treedy typically outperforms a previously proposed sorting-based heuristic.
PDF Link: /papers/13/p469-niinimaki.pdf
AUTHOR = "Teppo Niinimaki
and Mikko Koivisto",
TITLE = "Treedy: A Heuristic for Counting and Sampling Subsets",
BOOKTITLE = "Proceedings of the Twenty-Ninth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-13)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2013",
PAGES = "469--477"