Structuring Causal Tree Models with Continuous Variables
This extends the applicability of causal tree models, which are useful in evidential reasoning tasks, by addressing continuous variables.
The paper tackles the problem of structuring causal tree models for continuous variables by using auxiliary unobservable variables, showing that both the topology and internal relationships can be uncovered from pairwise dependencies under joint normal distribution, with less restrictive conditions than for binary variables.
This paper considers the problem of invoking auxiliary, unobservable variables to facilitate the structuring of causal tree models for a given set of continuous variables. Paralleling the treatment of bi-valued variables in [Pearl 1986], we show that if a collection of coupled variables are governed by a joint normal distribution and a tree-structured representation exists, then both the topology and all internal relationships of the tree can be uncovered by observing pairwise dependencies among the observed variables (i.e., the leaves of the tree). Furthermore, the conditions for normally distributed variables are less restrictive than those governing bi-valued variables. The result extends the applications of causal tree models which were found useful in evidential reasoning tasks.