Structuring Causal Tree Models with Continuous Variables
Lei Xu, Judea Pearl
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.
Keywords: Casual Tree Models, Evidential Reasoning
PDF Link: /papers/87/p170-xu.pdf
AUTHOR = "Lei Xu
and Judea Pearl",
TITLE = "Structuring Causal Tree Models with Continuous Variables",
BOOKTITLE = "Proceedings of the Third Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-87)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "1987",
PAGES = "170--179"