An Axiomatization of Loglinear Models with an Application to the Model-Search Problem
A good strategy to save computational time in a model-search problem consists in endowing the search procedure with a mechanism of logical inference, which sometimes allows a loglinear model to be accepted or rejected on logical grounds, without resorting to the numeric test. In principle, the best inferential mechanism should based on a complete axiomatization of loglinear models. We present a (probably incomplete) axiomatization, which can be translated into a graphical inference procedure working with directed acyclic graphs, and show how it can be applied to find an efficient solution to the model-search problem.
KeywordsDirected Acyclic Graph Inference Rule Conditional Independence Universal Model Loglinear Model
Unable to display preview. Download preview PDF.
- 6.Havranek, T., On application of statistical model search techniques in constructing a probabilistic knowledge base, Trans. 11th Prague Conf. on “Information Theory, Statistical Decision Functions and Random Processes” (1990).Google Scholar
- 7.Havranek, T., On model methods, Proc. 8th Symposium on “Computational Statistics” (1990).Google Scholar
- 8.Havranek, T., On model methods, Proc. Con. on “Symbolic-Numeric Data Analysis and Learning” (1991).Google Scholar
- 11.Malvestuto, F.M., Testing implication of hierarchical log-linear models for probability distributions, to appear in Statistics and Computing.Google Scholar
- 12.Malvestuto, F.M., Formal treatment of loglinear models for probability distributions, Proc. 3rd Workshop on “Uncertainty Processing in Expert Systems” (1994).Google Scholar
- 13.Malvestuto, F.M., Statistical versus relational join dependencies, Proc. 7th Int. Conf on “Scientific & Statistical Database Management” (1994).Google Scholar
- 14.Malvestuto, F.M., Formal theories of probabilistic dependency models, Proc. World Conf. on “Fundamentals of Artificial Intelligence” (1995).Google Scholar
- 15.Pearl, J., Probabilistic Reasoning in Intelligent Systems. Morgan Kaufman Pub., 1988.Google Scholar