This paper introduces a computational framework for reasoning in Bayesian belief networks that derives significant advantages from focused inference and relevance reasoning. This framework is based on d -separation and other simple and computationally efficient techniques for pruning irrelevant parts of a network. Our main contribution is a technique that we call relevance-based decomposition. Relevance-based decomposition approaches belief updating in large networks by focusing on their parts and decomposing them into partially overlapping subnetworks. This makes reasoning in some intractable networks possible and, in addition, often results in significant speedup, as the total time taken to update all subnetworks is in practice often considerably less than the time taken to update the network as a whole. We report results of empirical tests that demonstrate practical significance of our approach.

In most current applications of belief networks, domain knowledge is represented by a single belief network that applies to all problem instances in the domain. In more complex domains, problem-specific models must be constructed from a knowledge base encoding probabilistic relationships in the domain. Most work in knowledge-based model construction takes the rule as the basic unit of knowledge. We present a knowledge representation framework that permits the knowledge base designer to specify knowledge in larger semantically meaningful units which we call network fragments. Our framework provides for representation of asymmetric independence and canonical intercausal interaction. We discuss the combination of network fragments to form problem-specific models to reason about particular problem instances. The framework is illustrated using examples from the domain of military situation awareness.

The efficiency of inference in both the Hugin and, most notably, the Shafer-Shenoy architectures can be improved by exploiting the independence relations induced by the incoming messages of a clique. That is, the message to be sent from a clique can be computed via a factorization of the clique potential in the form of a junction tree. In this paper we show that by exploiting such nested junction trees in the computation of messages both space and time costs of the conventional propagation methods may be reduced. The paper presents a structured way of exploiting the nested junction trees technique to achieve such reductions. The usefulness of the method is emphasized through a thorough empirical evaluation involving ten large real-world Bayesian networks and the Hugin inference algorithm.

Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective computational procedures are represented by sequences possessing a special property; we shall call them perfect sequences. The paper lays down the elementary foundation necessary for further study of iterative application of operators of composition. We believe to develop a technique describing several graph models in a unifying way. We are convinced that practically all theoretical results and procedures connected with decomposable models and Bayesian networks can be translated into the terminology introduced in this paper. For example, complexity of computational procedures in these models is closely dependent on possibility to change the ordering of oligo-dimensional measures defining the model. Therefore, in this paper, lot of attention is paid to possibility to change ordering of the operators of composition.

A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is directly represented by a Bayesian network. By using a powerful way of specifying conditional probability distributions in these networks, the resulting formalism is more expressive than the previous ones. Particularly, it provides for constraints on equalities of events, and it allows to define complex, nested combination functions.

A pseudo independent (PI) model is a probabilistic domain model (PDM) where proper subsets of a set of collectively dependent variables display marginal independence. PI models cannot be learned correctly by many algorithms that rely on a single link search. Earlier work on learning PI models has suggested a straightforward multi-link search algorithm. However, when a domain contains recursively embedded PI submodels, it may escape the detection of such an algorithm. In this paper, we propose an improved algorithm that ensures the learning of all embedded PI submodels whose sizes are upper bounded by a predetermined parameter. We show that this improved learning capability only increases the complexity slightly beyond that of the previous algorithm. The performance of the new algorithm is demonstrated through experiment.

We review the problem of time-critical action and discuss a reformulation that shifts knowledge acquisition from the assessment of complex temporal probabilistic dependencies to the direct assessment of time-dependent utilities over key outcomes of interest. We dwell on a class of decision problems characterized by the centrality of diagnosing and reacting in a timely manner to pathological processes. We motivate key ideas in the context of trauma-care triage and transportation decisions.

We describe work to control graphics rendering under limited computational resources by taking a decision-theoretic perspective on perceptual costs and computational savings of approximations. The work extends earlier work on the control of rendering by introducing methods and models for computing the expected cost associated with degradations of scene components. The expected cost is computed by considering the perceptual cost of degradations and a probability distribution over the attentional focus of viewers. We review the critical literature describing findings on visual search and attention, discuss the implications of the findings, and introduce models of expected perceptual cost. Finally, we discuss policies that harness information about the expected cost of scene components.

Valuation based systems verifying an idempotent property are studied. A partial order is defined between the valuations giving them a lattice structure. Then, two different strategies are introduced to represent valuations: as infimum of the most informative valuations or as supremum of the least informative ones. It is studied how to carry out computations with both representations in an efficient way. The particular cases of finite sets and convex polytopes are considered.

Decision theory has become widely accepted in the AI community as a useful framework for planning and decision making. Applying the framework typically requires elicitation of some form of probability and utility information. While much work in AI has focused on providing representations and tools for elicitation of probabilities, relatively little work has addressed the elicitation of utility models. This imbalance is not particularly justified considering that probability models are relatively stable across problem instances, while utility models may be different for each instance. Spending large amounts of time on elicitation can be undesirable for interactive systems used in low-stakes decision making and in time-critical decision making. In this paper we investigate the issues of reasoning with incomplete utility models. We identify patterns of problem instances where plans can be proved to be suboptimal if the (unknown) utility function satisfies certain conditions. We present an approach to planning and decision making that performs the utility elicitation incrementally and in a way that is informed by the domain model.