TR-153: The Use of Chi-Squared Statistics in Determining Dependence Trees

Abstract

In several pattern-recognition applications, it is often neccesary to approximate prob­ability distributions with well defined, parametrized q.ensity functions. For the case of discrete-valued functions (and for the cases when the features are not necessarily normally distributed), a method known as the dependence-tree exists. This method is based on the metric known as the Expected Mutual Information Measure. This paper studies the suitability of a chi-squared based metric for the same purpose. For a restricted class of distributions, these two metrics are shown to be equivalent and stochastically optimal. For the general cases, the latter metric is almost as efficient as the optimal one, but is computationally far superior.