Perfect Tree-Like Markovian Distributions
Ann Becker, Dan Geiger, Christopher Meek
We show that if a strictly positive joint probability distribution for a set of binary random variables factors according to a tree, then vertex separation represents all and only the independence relations enclosed in the distribution. The same result is shown to hold also for multivariate strictly positive normal distributions. Our proof uses a new property of conditional independence that holds for these two classes of probability distributions.
PDF Link: /papers/00/p19-becker.pdf
AUTHOR = "Ann Becker
and Dan Geiger and Christopher Meek",
TITLE = "Perfect Tree-Like Markovian Distributions",
BOOKTITLE = "Proceedings of the Sixteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-00)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "2000",
PAGES = "19--23"