Credal Networks under Maximum Entropy
We apply the principle of maximum entropy to select a unique joint probability distribution from the set of all joint probability distributions specified by a credal network. In detail, we start by showing that the unique joint distribution of a Bayesian tree coincides with the maximum entropy model of its conditional distributions. This result, however, does not hold anymore for general Bayesian networks. We thus present a new kind of maximum entropy models, which are computed sequentially. We then show that for all general Bayesian networks, the sequential maximum entropy model coincides with the unique joint distribution. Moreover, we apply the new principle of sequential maximum entropy to interval Bayesian networks and more generally to credal networks. We especially show that this application is equivalent to a number of small local entropy maximizations.
Keywords: credal networks, interval Bayesian networks, Bayesian networks, maximum entropy
PS Link: http://www.kr.tuwien.ac.at/staff/lukasiew/uai00.ps.gz
PDF Link: /papers/00/p363-lukasiewicz.pdf
AUTHOR = "Thomas Lukasiewicz
TITLE = "Credal Networks under Maximum Entropy",
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 = "363--370"