DMCA
Approximating discrete probability distributions with dependence trees (1968)
| Venue: | IEEE TRANSACTIONS ON INFORMATION THEORY |
| Citations: | 878 - 0 self |
BibTeX
@ARTICLE{Chow68approximatingdiscrete,
author = {C. K. Chow and C. N. Liu},
title = {Approximating discrete probability distributions with dependence trees},
journal = {IEEE TRANSACTIONS ON INFORMATION THEORY},
year = {1968},
volume = {14},
number = {3},
pages = {462--467}
}
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Abstract
A method is presented to approximate optimally an n-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 of n-1 first order dependence relationship among the n variables. 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.
Keyphrases
dependence tree discrete probability distribution optimum set maximum-likelihood estimate unknown distribution n-1 first order dependence relationship minimum difference n-dimensional discrete probability distribution tree dependence empirical observation second-order distribution first-order tree dependence
