DAVID: Influence Diagram Processing System for the Macintosh

Influence diagrams are a directed graph representation for uncertainties as probabilities. The graph distinguishes between those variables which are under the control of a decision maker (decisions, shown as rectangles) and those which are not (chances, shown as ovals), as well as explicitly denoting a goal for solution (value, shown as a rounded rectangle.Comment: Appears in Proceedings of the Second Conference on Uncertainty in Artificial Intelligence (UAI1986

Integrating Logical and Probabilistic Reasoning for Decision Making

We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and solution of probabilistic and decision-theoretic models for complex and uncertain domains. Given a query, a logical proof is produced if possible; if not, an influence diagram based on the query and the knowledge of the decision domain is produced and subsequently solved. A uniform declarative, first-order, knowledge representation is combined with a set of integrated inference procedures for logical, probabilistic, and decision-theoretic reasoning.Comment: Appears in Proceedings of the Third Conference on Uncertainty in Artificial Intelligence (UAI1987

A Method for Using Belief Networks as Influence Diagrams

This paper demonstrates a method for using belief-network algorithms to solve influence diagram problems. In particular, both exact and approximation belief-network algorithms may be applied to solve influence-diagram problems. More generally, knowing the relationship between belief-network and influence-diagram problems may be useful in the design and development of more efficient influence diagram algorithms.Comment: Appears in Proceedings of the Fourth Conference on Uncertainty in Artificial Intelligence (UAI1988

Causal Networks: Semantics and Expressiveness

Dependency knowledge of the form "x is independent of y once z is known" invariably obeys the four graphoid axioms, examples include probabilistic and database dependencies. Often, such knowledge can be represented efficiently with graphical structures such as undirected graphs and directed acyclic graphs (DAGs). In this paper we show that the graphical criterion called d-separation is a sound rule for reading independencies from any DAG based on a causal input list drawn from a graphoid. The rule may be extended to cover DAGs that represent functional dependencies as well as conditional dependencies.Comment: Appears in Proceedings of the Fourth Conference on Uncertainty in Artificial Intelligence (UAI1988

ARCO1: An Application of Belief Networks to the Oil Market

Belief networks are a new, potentially important, class of knowledge-based models. ARCO1, currently under development at the Atlantic Richfield Company (ARCO) and the University of Southern California (USC), is the most advanced reported implementation of these models in a financial forecasting setting. ARCO1's underlying belief network models the variables believed to have an impact on the crude oil market. A pictorial market model-developed on a MAC II- facilitates consensus among the members of the forecasting team. The system forecasts crude oil prices via Monte Carlo analyses of the network. Several different models of the oil market have been developed; the system's ability to be updated quickly highlights its flexibility.Comment: Appears in Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence (UAI1991

Computation of Variances in Causal Networks

The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks, often treat the conditional probabilities which are stored in the network as certain values. However, if one takes either a subjectivistic or a limiting frequency approach to probability, one can never be certain of probability values. An algorithm for probabilistic inference should not only be capable of reporting the inferred probabilities; it should also be capable of reporting the uncertainty in these probabilities relative to the uncertainty in the probabilities which are stored in the network. In section 2 of this paper a method is given for determining the prior variances of the probabilities of all the nodes. Section 3 contains an approximation method for determining the variances in inferred probabilities.Comment: Appears in Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence (UAI1990

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

Dynamic Network Updating Techniques For Diagnostic Reasoning

A new probabilistic network construction system, DYNASTY, is proposed for diagnostic reasoning given variables whose probabilities change over time. Diagnostic reasoning is formulated as a sequential stochastic process, and is modeled using influence diagrams. Given a set O of observations, DYNASTY creates an influence diagram in order to devise the best action given O. Sensitivity analyses are conducted to determine if the best network has been created, given the uncertainty in network parameters and topology. DYNASTY uses an equivalence class approach to provide decision thresholds for the sensitivity analysis. This equivalence-class approach to diagnostic reasoning differentiates diagnoses only if the required actions are different. A set of network-topology updating algorithms are proposed for dynamically updating the network when necessary.Comment: Appears in Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence (UAI1991

Mixtures of Gaussians and Minimum Relative Entropy Techniques for Modeling Continuous Uncertainties

Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is to fit analytically tractable continuous probability distributions. This approach has potential simplicity and accuracy advantages, especially if variables can be transformed first. This paper shows how a minimum relative entropy criterion can drive both transformation and fitting, illustrating with a power and logarithm family of transformations and mixtures of Gaussian (normal) distributions, which allow use of efficient influence diagram methods. The fitting procedure in this case is the well-known EM algorithm. The selection of the number of components in a fitted mixture distribution is automated with an objective that trades off accuracy and computational cost.Comment: Appears in Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI1993

A Graph-Based Inference Method for Conditional Independence

The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such axioms provide a mechanism for manipulating conditional independence assertions without resorting to their numerical definition. This paper explores a representation for independence statements using multiple undirected graphs and some simple graphical transformations. The independence statements derivable in this system are equivalent to those obtainable by the graphoid axioms. Therefore, this is a purely graphical proof technique for conditional independence.Comment: Appears in Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence (UAI1991