F. J. Díez and M. J. Druzdzel. Canonical probabilistic models for knowledge engineering. Technical Report CISIAD-06-01. UNED, Madrid, 2006.
59 pages. PDF (449 KB), BibTeX entry.
The hardest task in knowledge engineering for probabilistic graphical models, such as Bayesian networks and influence diagrams, is obtaining their numerical parameters. Models based on acyclic directed graphs and composed of discrete variables, currently most common in practice, require for every variable a number of parameters that is exponential in the number of its parents in the graph, which makes elicitation from experts or learning from databases a daunting task. In this paper, we review the so called canonical models whose main advantage is that they require much fewer parameters. We propose a general framework for them, based on three categories: deterministic models, ICI models, and simple canonical models. ICI models rely on the concept of independence of causal influence, and can be subdivided into noisy and leaky. We then analyze the most common families of canonical models (the OR/MAX, the AND/MIN, and the noisy XOR), generalizing them and offering criteria for applying them in practice. We also briefly review temporal canonical models.