Hybrid Influence Diagrams Using Mixtures of Truncated Exponentials
This work addresses decision-making problems in probabilistic graphical models by enabling more flexible hybrid representations, though it appears incremental as it builds on existing MTE potentials.
The paper tackles the problem of representing continuous chance variables and utility functions in influence diagrams without restrictions on relationships, distributions, or utility nature, by introducing MTE influence diagrams and solving them with a variable elimination fusion algorithm.
Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization for representing continuous chance variables in influence diagrams. Also, MTE potentials can be used to approximate utility functions. This paper introduces MTE influence diagrams, which can represent decision problems without restrictions on the relationships between continuous and discrete chance variables, without limitations on the distributions of continuous chance variables, and without limitations on the nature of the utility functions. In MTE influence diagrams, all probability distributions and the joint utility function (or its multiplicative factors) are represented by MTE potentials and decision nodes are assumed to have discrete state spaces. MTE influence diagrams are solved by variable elimination using a fusion algorithm.