We investigate the value of extending the completeness of a decision model along different dimensions of refinement. Specifically, we analyze the expected value of quantitative, conceptual, and structural refinement of decision models. We illustrate the key dimensions of refinement with examples. The analyses of value of model refinement can be used to focus the attention of an analyst or an automated reasoning system on extensions of a decision model associated with the greatest expected value.

Probabilistic conceptual network is a knowledge representation scheme designed for reasoning about concepts and categorical abstractions in utility-based categorization. The scheme combines the formalisms of abstraction and inheritance hierarchies from artificial intelligence, and probabilistic networks from decision analysis. It provides a common framework for representing conceptual knowledge, hierarchical knowledge, and uncertainty. It facilitates dynamic construction of categorization decision models at varying levels of abstraction. The scheme is applied to an automated machining problem for reasoning about the state of the machine at varying levels of abstraction in support of actions for maintaining competitiveness of the plant.

This paper identifies and solves a new optimization problem: Given a belief network (BN) and a target ordering on its variables, how can we efficiently derive its minimal I-map whose arcs are consistent with the target ordering? We present three solutions to this problem, all of which lead to directed acyclic graphs based on the original BN's recursive basis relative to the specified ordering (such a DAG is sometimes termed the boundary DAG drawn from the given BN relative to the said ordering [5]). Along the way, we also uncover an important general principal about arc reversals: when reordering a BN according to some target ordering, (while attempting to minimize the number of arcs generated), the sequence of arc reversals should follow the topological ordering induced by the original belief network's arcs to as great an extent as possible. These results promise to have a significant impact on the derivation of consensus models, as well as on other algorithms that require the reconfiguration and/or combination of BN's.

One topic that is likely to attract an increasing amount of attention within the Knowledge-base systems resesearch community is the coordination of information provided by multiple experts. We envision a situation in which several experts independently encode information as belief networks. A potential user must then coordinate the conclusions and recommendations of these networks to derive some sort of consensus. One approach to such a consensus is the fusion of the contributed networks into a single, consensus model prior to the consideration of any case-specific data (specific observations, test results). This approach requires two types of combination procedures, one for probabilities, and one for graphs. Since the combination of probabilities is relatively well understood, the key barriers to this approach lie in the realm of graph theory. This paper provides formal definitions of some of the operations necessary to effect the necessary graphical combinations, and provides complexity analyses of these procedures. The paper's key result is that most of these operations are NPhard, and its primary message is that the derivation of "good" consensus networks must be done heuristically. to several general frameworks for knowledge bases, including production rules, frames, formal logic, and belief networks (BN's). It has also helped raise several topics that promise to become increasingly important in the next wave of research.

Causal Models are like Dependency Graphs and Belief Nets in that they provide a structure and a set of assumptions from which a joint distribution can, in principle, be computed. Unlike Dependency Graphs, Causal Models are models of hierarchical and/or parallel processes, rather than models of distributions (partially) known to a model builder through some sort of gestalt. As such, Causal Models are more modular, easier to build, more intuitive, and easier to understand than Dependency Graph Models. Causal Models are formally defined and Dependency Graph Models are shown to be a special case of them. Algorithms supporting inference are presented. Parsimonious methods for eliciting dependent probabilities are presented.

When eliciting probability models from experts, knowledge engineers may compare the results of the model with expert judgment on test scenarios, then adjust model parameters to bring the behavior of the model more in line with the expert's intuition. This paper presents a methodology for analytic computation of sensitivity values to measure the impact of small changes in a network parameter on a target probability value or distribution. These values can be used to guide knowledge elicitation. They can also be used in a gradient descent algorithm to estimate parameter values that maximize a measure of goodness-of-fit to both local and holistic probability assessments.

We take a utility-based approach to categorization. We construct generalizations about events and actions by considering losses associated with failing to distinguish among detailed distinctions in a decision model. The utility-based methods transform detailed states of the world into more abstract categories comprised of disjunctions of the states. We show how we can cluster distinctions into groups of distinctions at progressively higher levels of abstraction, and describe rules for decision making with the abstractions. The techniques introduce a utility-based perspective on the nature of concepts, and provide a means of simplifying decision models used in automated reasoning systems. We demonstrate the techniques by describing the capabilities and output of TUBA, a program for utility-based abstraction.

Relational models for diagnosis are based on a direct description of the association between disorders and manifestations. This type of model has been specially used and developed by Reggia and his co-workers in the late eighties as a basic starting point for approaching diagnosis problems. The paper proposes a new relational model which includes Reggia's model as a particular case and which allows for a more expressive representation of the observations and of the manifestations associated with disorders. The model distinguishes, i) between manifestations which are certainly absent and those which are not (yet) observed, and ii) between manifestations which cannot be caused by a given disorder and manifestations for which we do not know if they can or cannot be caused by this disorder. This new model, which can handle uncertainty in a non-probabilistic way, is based on possibility theory and so-called twofold fuzzy sets, previously introduced by the authors.

Spiegelhalter and Lauritzen [15] studied sequential learning in Bayesian networks and proposed three models for the representation of conditional probabilities. A forth model, shown here, assumes that the parameter distribution is given by a product of Gaussian functions and updates them from the _ and _r messages of evidence propagation. We also generalize the noisy OR-gate for multivalued variables, develop the algorithm to compute probability in time proportional to the number of parents (even in networks with loops) and apply the learning model to this gate.

The inherent intractability of probabilistic inference has hindered the application of belief networks to large domains. Noisy ORgates [30] and probabilistic similarity networks [18, 17) escape the complexity of inference by restricting model expressiveness. Recent work in the application of belief-network models to time-series analysis and forecasting [9, 10) has given rise to the additive beliefnetwork model (ABNM). We (1) discuss the nature and implications of the approximations made by an additive decomposition of a belief network, (2) show greater efficiency in the induction of additive models when available data are scarce, (3) generalize probabilistic inference algorithms to exploit the additive decomposition of ABNMs, (4) show greater efficiency of inference, and (5) compare results on inference with a simple additive belief network.