A Copulas-Based Approach to Modeling Dependence in Decision Trees

Summary:

Tianyang Wang and James S. Dyer used a copula function as a basis for decision trees; these copulas contained parameters that were demonstrated through probability trees, which are discreet and conditional. 

The process of using a dependent decision tree is:

1.      Assessment of marginals, dependence, and copula. During this step, the authors state the need to assess the information available as well as determine what type of copula is best used for the dependence and existence of uncertainties. Statistical measures are used to go through the variables and determine to correct copula.

2.      Specification of parameters for the underlying copula. In order to use the copula in a dependency structure, parameters need to be established. For the elliptical copula parameters can be established through an estimate of the correlation between original uncertainties.

3.      Construction of the transient tree structure for underlying copula. The resulting process is a probability tree that uses the conditional probability that was established.

4.      Point-to-point inverse marginal transformation. This step uses different distributions to draw out the tree

From this process, decision trees are drawn out for various outcomes and the decision tree model is applied to various forms of copulas.

Critique:

This study provided an interesting application of decision trees.  Not only did the study illustrate the various potential outcomes, but it also broke down the process into specific steps.  While the application was not directly related to the intelligence field, the process of organizing and structuring decision trees.  This process was specifically geared towards copulas and creating a dependant tree, though there is an issue with the fact that there can be a significantly large number of variables that grow form the initial construct. The base of the tree is set from parameters established through equations.  While this application of a decision tree is effective for this purpose, it is difficult to gain a deep understanding of the concept in relation to non-statistical elements.  Decision trees are useful to gain a broad understanding of various different outcomes and they have the potential to be an effective initial step in an analysis of information.

This methodology appears to be useful in a statistical application, though this study does not directly demonstrate the application from an intelligence stand-point.

Wang, T. & Dyer J. S. (2012). A Copulas-Based Approach to Modeling Dependence in Decision Trees. Operations Research, 60(1), 225-42.