## Credal Sets Approximation by Lower Probabilities: Application to Credal Networks

**Authors: **Alessandro Antonucci and Fabio Cuzzolin

**Abstract:** Credal sets are closed convex sets of probability mass functions.
The lower probabilities specified by a credal set for each element
of the power set can be used as constraints defining a second credal
set. This simple procedure produces an outer approximation, with
a bounded number of extreme points, for general credal sets. The
approximation is optimal in the sense that no other lower probabilities
can specify smaller supersets of the original credal set. Notably,
in order to be computed, the approximation does not need the extreme
points of the credal set, but only its lower probabilities. This
makes the approximation particularly suited for credal networks,
which are a generalization of Bayesian networks based on credal sets.
Although most of the algorithms for credal networks updating only
return lower posterior probabilities, the suggested approximation
can be used to evaluate (as an outer approximation of) the posterior
credal set. This makes it possible to adopt more sophisticated decision
making criteria, without having to replace existing algorithms. The
quality of the approximation is investigated by numerical tests.

**Year:** 2010.

**Details:** In Hüllermeier, E. and Kruse, R. and Hoffmann, F. (Eds.), *Computational Intelligence for Knowledge-Based Systems Design, 13th
International Conference on Information Processing and Management
of Uncertainty, IPMU 2010, Dortmund, Germany, June 28 - July 2, 2010.
Proceedings*. Springer, pp. 716-725.

A version similar to the published paper can be downloaded.