Hybrid Influence Diagrams Using Mixtures of Truncated Exponentials

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.Comment: Appears in Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI2004

Solving Hybrid Influence Diagrams with Deterministic Variables

We describe a framework and an algorithm for solving hybrid influence diagrams with discrete, continuous, and deterministic chance variables, and discrete and continuous decision variables. A continuous chance variable in an influence diagram is said to be deterministic if its conditional distributions have zero variances. The solution algorithm is an extension of Shenoy's fusion algorithm for discrete influence diagrams. We describe an extended Shenoy-Shafer architecture for propagation of discrete, continuous, and utility potentials in hybrid influence diagrams that include deterministic chance variables. The algorithm and framework are illustrated by solving two small examples.Comment: Appears in Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence (UAI2010

IDEAL: A Software Package for Analysis of Influence Diagrams

IDEAL (Influence Diagram Evaluation and Analysis in Lisp) is a software environment for creation and evaluation of belief networks and influence diagrams. IDEAL is primarily a research tool and provides an implementation of many of the latest developments in belief network and influence diagram evaluation in a unified framework. This paper describes IDEAL and some lessons learned during its development.Comment: Appears in Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence (UAI1990

Solving Multistage Influence Diagrams using Branch-and-Bound Search

A branch-and-bound approach to solving influ- ence diagrams has been previously proposed in the literature, but appears to have never been implemented and evaluated - apparently due to the difficulties of computing effective bounds for the branch-and-bound search. In this paper, we describe how to efficiently compute effective bounds, and we develop a practical implementa- tion of depth-first branch-and-bound search for influence diagram evaluation that outperforms existing methods for solving influence diagrams with multiple stages.Comment: Appears in Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence (UAI2010

Using Potential Influence Diagrams for Probabilistic Inference and Decision Making

The potential influence diagram is a generalization of the standard "conditional" influence diagram, a directed network representation for probabilistic inference and decision analysis [Ndilikilikesha, 1991]. It allows efficient inference calculations corresponding exactly to those on undirected graphs. In this paper, we explore the relationship between potential and conditional influence diagrams and provide insight into the properties of the potential influence diagram. In particular, we show how to convert a potential influence diagram into a conditional influence diagram, and how to view the potential influence diagram operations in terms of the conditional influence diagram.Comment: Appears in Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI1993

Information/Relevance Influence Diagrams

In this paper we extend the influence diagram (ID) representation for decisions under uncertainty. In the standard ID, arrows into a decision node are only informational; they do not represent constraints on what the decision maker can do. We can represent such constraints only indirectly, using arrows to the children of the decision and sometimes adding more variables to the influence diagram, thus making the ID more complicated. Users of influence diagrams often want to represent constraints by arrows into decision nodes. We represent constraints on decisions by allowing relevance arrows into decision nodes. We call the resulting representation information/relevance influence diagrams (IRIDs). Information/relevance influence diagrams allow for direct representation and specification of constrained decisions. We use a combination of stochastic dynamic programming and Gibbs sampling to solve IRIDs. This method is especially useful when exact methods for solving IDs fail.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

Solving Asymmetric Decision Problems with Influence Diagrams

While influence diagrams have many advantages as a representation framework for Bayesian decision problems, they have a serious drawback in handling asymmetric decision problems. To be represented in an influence diagram, an asymmetric decision problem must be symmetrized. A considerable amount of unnecessary computation may be involved when a symmetrized influence diagram is evaluated by conventional algorithms. In this paper we present an approach for avoiding such unnecessary computation in influence diagram evaluation.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

From influence diagrams to multi-operator cluster DAGs

There exist several architectures to solve influence diagrams using local computations, such as the Shenoy-Shafer, the HUGIN, or the Lazy Propagation architectures. They all extend usual variable elimination algorithms thanks to the use of so-called 'potentials'. In this paper, we introduce a new architecture, called the Multi-operator Cluster DAG architecture, which can produce decompositions with an improved constrained induced-width, and therefore induce potentially exponential gains. Its principle is to benefit from the composite nature of influence diagrams, instead of using uniform potentials, in order to better analyze the problem structure.Comment: Appears in Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence (UAI2006

Representing and Solving Asymmetric Bayesian Decision Problems

This paper deals with the representation and solution of asymmetric Bayesian decision problems. We present a formal framework, termed asymmetric influence diagrams, that is based on the influence diagram and allows an efficient representation of asymmetric decision problems. As opposed to existing frameworks, the asymmetric influece diagram primarily encodes asymmetry at the qualitative level and it can therefore be read directly from the model. We give an algorithm for solving asymmetric influence diagrams. The algorithm initially decomposes the asymmetric decision problem into a structure of symmetric subproblems organized as a tree. A solution to the decision problem can then be found by propagating from the leaves toward the root using existing evaluation methods to solve the sub-problems.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000

From Influence Diagrams to Junction Trees

We present an approach to the solution of decision problems formulated as influence diagrams. This approach involves a special triangulation of the underlying graph, the construction of a junction tree with special properties, and a message passing algorithm operating on the junction tree for computation of expected utilities and optimal decision policies.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994