Approximating discrete probability distributions with dependence trees
Abstract:
A
method is presented to approximate optimally ann-dimensional discrete
probability distribution by a product of second-order distributions, or
the distribution of the first-order tree dependence. The problem is to
find an optimum set ofn - 1first order dependence relationship among
thenvariables. It is shown that the procedure derived in this paper
yields an approximation of a minimum difference in information. It is
further shown that when this procedure is applied to empirical
observations from an unknown distribution of tree dependence, the
procedure is the maximum-likelihood estimate of the distribution.
Published in:
IEEE Transactions on Information Theory
(
Volume: 14, Issue: 3, May 1968
)
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