Canonical Probabilistic Models for Knowledge Engineering

The hardest task in knowledge engineering for probabilistic graphical models, such as Bayesian networks and in∞uence 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 in∞uence 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 ofiering criteria for applying them in practice. We also brie∞y review temporal canonical models.