Practically Perfect
Christopher Meek, David Chickering
Abstract:
The property of perfectness plays an important role in the theory of Bayesian networks. First, the existence of perfect distributions for arbitrary sets of variables and directed acyclic graphs implies that various methods for reading independence from the structure of the graph (e.g., Pearl, 1988; Lauritzen, Dawid, Larsen & Leimer, 1990) are complete. Second, the asymptotic reliability of various search methods is guaranteed under the assumption that the generating distribution is perfect (e.g., Spirtes, Glymour & Scheines, 2000; Chickering & Meek, 2002). We provide a lowerbound on the probability of sampling a nonperfect distribution when using a fixed number of bits to represent the parameters of the Bayesian network. This bound approaches zero exponentially fast as one increases the number of bits used to represent the parameters. This result implies that perfect distributions with fixedlength representations exist. We also provide a lowerbound on the number of bits needed to guarantee that a distribution sampled from a uniform Dirichlet distribution is perfect with probability greater than 1/2. This result is useful for constructing randomized reductions for hardness proofs.
Keywords:
Pages: 411416
PS Link:
PDF Link: /papers/03/p411meek.pdf
BibTex:
@INPROCEEDINGS{Meek03,
AUTHOR = "Christopher Meek
and David Chickering",
TITLE = "Practically Perfect",
BOOKTITLE = "Proceedings of the Nineteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI03)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "2003",
PAGES = "411416"
}

