Local computations with probabilities on graphical structures and their application to expert systems. (English) Zbl 0684.68106

Lauritzen, S. L.; Spiegelhalter, D. J.

J. R. Stat. Soc., Ser. B 50, No. 2, 157-224 (1988).

The presented paper is one of the basic contributions to uncertain knowledge management in expert systems which is based on the probability theory. Likewise in other probabilistic models, input pieces of knowledge are assumed to be in a form of some conditional probabilities and the corresponding joint multidimensional distribution comprehends all the knowledge from the area of interest. An extensive theory is presented which solves the main problem: how to cope with representation and utiliztion of probability distributions of high dimensions? There are two basic ideas the approach is based on. One is the use of graphical representation of the distributions the other issues from the possibility to neglect all the information which does not influence resulting conditional probabilities - to compute these probabilities locally.
The paper contains both wide philosophical and methodological discussions and extensive references. Being supplemented by a discussion, in which 45 specialists took part, the paper is thus one of the contributions which can serve as a basic source for detailed study of possibilities offered by the probability theory to the field of artificial intelligence.

Reviewer: R.Jiroušek

MSC:

68T99	Artificial intelligence
60E99	Distribution theory

Keywords:

Bayesian methods; triangulated graphs; expert systems