As belief networks are used to model increasingly complex situations, the need to automatically construct them from large databases will become paramount. This paper concentrates on solving a part of the belief network induction problem: that of learning the quantitative structure (the conditional probabilities), given the qualitative structure. In particular, a theory is presented that shows how to propagate inference distributions in a belief network, with the only assumption being that the given qualitative structure is correct. Most inference algorithms must make at least this assumption. The theory is based on four network transformations that are sufficient for any inference in a belief network. Furthermore, the claim is made that contrary to popular belief, error will not necessarily grow as the inference chain grows. Instead, for QBN belief nets induced from large enough samples, the error is more likely to decrease as the size of the inference chain increases.

One of the most difficult aspects of modeling complex dilemmas in decision-analytic terms is composing a diagram of relevance relations from a set of domain concepts. Decision models in domains such as medicine, however, exhibit certain prototypical patterns that can guide the modeling process. Medical concepts can be classified according to semantic types that have characteristic positions and typical roles in an influence-diagram model. We have developed a graph-grammar production system that uses such inherent interrelationships among medical terms to f9-cilitate the modeling of medical decisions.

PAGODA (Probabilistic Autonomous Goal-Directed Agent) is a model for autonomous learning in probabilistic domains [desJardins, 1992] that incorporates innovative techniques for using the agent's existing knowledge to guide and constrain the learning process and for representing, reasoning with, and learning probabilistic knowledge. This paper describes the probabilistic representation and inference mechanism used in PAGODA. PAGODA forms theories about the effects of its actions and the world state on the environment over time. These theories are represented as conditional probability distributions. A restriction is imposed on the structure of the theories that allows the inference mechanism to find a unique predicted distribution for any action and world state description. These restricted theories are called uniquely predictive theories. The inference mechanism, Probability Combination using Independence (PCI), uses minimal independence assumptions to combine the probabilities in a theory to make probabilistic predictions.

We present a mechanism for constructing graphical models, specifically Bayesian networks, from a knowledge base of general probabilistic information. The unique feature of our approach is that it uses a powerful first-order probabilistic logic for expressing the general knowledge base. This logic allows for the representation of a wide range of logical and probabilistic information. The model construction procedure we propose uses notions from direct inference to identify pieces of local statistical information from the knowledge base that are most appropriate to the particular event we want to reason about. These pieces are composed to generate a joint probability distribution specified as a Bayesian network. Although there are fundamental difficulties in dealing with fully general knowledge, our procedure is practical for quite rich knowledge bases and it supports the construction of a far wider range of networks than allowed for by current template technology.

The Noisy-Or model is convenient for describing a class of uncertain relationships in Bayesian networks [Pearl 1988]. Pearl describes the Noisy-Or model for Boolean variables. Here we generalize the model to nary input and output variables and to arbitrary functions other than the Boolean OR function. This generalization is a useful modeling aid for construction of Bayesian networks. We illustrate with some examples including digital circuit diagnosis and network reliability analysis.

Relevance-based explanation is a scheme in which partial assignments to Bayesian belief network variables are explanations (abductive conclusions). We allow variables to remain unassigned in explanations as long as they are irrelevant to the explanation, where irrelevance is defined in terms of statistical independence. When multiple-valued variables exist in the system, especially when subsets of values correspond to natural types of events, the overspecification problem, alleviated by independence-based explanation, resurfaces. As a solution to that, as well as for addressing the question of explanation specificity, it is desirable to collapse such a subset of values into a single value on the fly. The equivalent method, which is adopted here, is to generalize the notion of assignments to allow disjunctive assignments. We proceed to define generalized independence based explanations as maximum posterior probability independence based generalized assignments (GIB-MAPs). GIB assignments are shown to have certain properties that ease the deJ ign of algorithms for computing GIB-MAPs. One such algorithm is discussed here, as well as suggestions for how other algorithms may be adapted to compute GIB-MAPs. GIB-MAP explanations still suffer from instability, a problem which may be addressed using "approximate" conditional independence as a condition for irrelevance.

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.

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.