Perfect Tree-like Markovian Distributions
Abstract
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 encoded 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.
Cite
Text
Becker et al. "Perfect Tree-like Markovian Distributions." Conference on Uncertainty in Artificial Intelligence, 2000.Markdown
[Becker et al. "Perfect Tree-like Markovian Distributions." Conference on Uncertainty in Artificial Intelligence, 2000.](https://mlanthology.org/uai/2000/becker2000uai-perfect/)BibTeX
@inproceedings{becker2000uai-perfect,
title = {{Perfect Tree-like Markovian Distributions}},
author = {Becker, Ann and Geiger, Dan and Meek, Christopher},
booktitle = {Conference on Uncertainty in Artificial Intelligence},
year = {2000},
pages = {19-23},
url = {https://mlanthology.org/uai/2000/becker2000uai-perfect/}
}