Hybrid Influence Diagrams Using Mixtures of Truncated Exponentials

TL;DR

This paper introduces MTE influence diagrams that utilize mixtures of truncated exponentials to represent continuous variables and utilities, enabling flexible and unrestricted decision modeling.

Contribution

It presents a novel framework for influence diagrams using MTE potentials, allowing for unrestricted relationships and distributions among variables.

Findings

MTE influence diagrams can model complex decision problems with continuous variables.

The fusion algorithm efficiently solves MTE influence diagrams.

The approach generalizes existing influence diagram methods to continuous domains.

Abstract

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.