Rs. Valiveti et Bj. Oommen, DETERMINING STOCHASTIC DEPENDENCE FOR NORMALLY DISTRIBUTED VECTORS USING THE CHI-SQUARED METRIC, Pattern recognition, 26(6), 1993, pp. 975-987
Citations number
10
Categorie Soggetti
Computer Sciences, Special Topics","Engineering, Eletrical & Electronic","Computer Applications & Cybernetics
A fundamental problem in information theory and pattern recognition in
volves computing and estimating the probability density function assoc
iated with a set of random variables. In estimating this density funct
ion, one can either assume that the form of the density function is kn
own, and that we are merely estimating parameters that characterize th
e distribution or that no information about the density function is av
ailable. This problem has been extensively studied if the random varia
bles are independent. If the random variables are dependent and are of
the discrete sort, the problem of capturing this dependence between v
ariables has been studied in Chow and Liu (IEEE Trans. Inf. Theory 14,
462-467 (May 1968)). The analogous problem for normally distributed c
ontinuous random variables has been tackled in Chow et al. (Comput. Bi
omed. Res. 12, 589-613 (1979)). In both these instances, the determina
tion of the best dependence tree hinges on the well-known Expected Mut
ual Information Measure (EMIM) Metric. Recently Valiveti and Oommen st
udied the suitability of the chi-squared based metric in-lieu of the E
MIM metric, for the discrete variable case (Pattern Recognition 25. 13
89-1400 (1992)). In this paper, we generalize the latter result and st
udy the use of the chi-squared metric for determining dependence trees
for normally distributed random vectors. We show that for such vector
s, the chi-squared metric yields the optimal tree and that it is ident
ical to the one obtained using the EMIM metric. The computation of the
maximum likelihood estimate of the dependence tree is also discussed.