This paper discusses how conflicts (as used by the consistency-based diagnosis community) can be adapted to be used in a search-based algorithm for computing prior and posterior probabilities in discrete Bayesian Networks. This is an "anytime" algorithm, that at any stage can estimate the probabilities and give an error bound. Whereas the most popular Bayesian net algorithms exploit the structure of the network for efficiency, we exploit probability distributions for efficiency; this algorithm is most suited to the case with extreme probabilities. This paper presents a solution to the inefficiencies found in naive algorithms, and shows how the tools of the consistency-based diagnosis community (namely conflicts) can be used effectively to improve the efficiency. Empirical results with networks having tens of thousands of nodes are presented.

This paper describes ongoing research into planning in an uncertain environment. In particular, it introduces U-Plan, a planning system that constructs quantitatively ranked plans given an incomplete description of the state of the world. U-Plan uses a DempsterShafer interval to characterise uncertain and incomplete information about the state of the world. The planner takes as input what is known about the world, and constructs a number of possible initial states with representations at different abstraction levels. A plan is constructed for the initial state with the greatest support, and this plan is tested to see if it will work for other possible initial states. All, part, or none of the existing plans may be used in the generation of the plans for the remaining possible worlds. Planning takes place in an abstraction hierarchy where strategic decisions are made before tactical decisions. A super-plan is then constructed, based on merging the set of plans and the appropriately timed acquisition of essential knowledge, which is used to decide between plan alternatives. U-Plan usually produces a super-plan in less time than a classical planner would take to produce a set of plans, one for each possible world.

Two algorithms are presented for "compiling" influence diagrams into a set of simple decision rules. These decision rules define simple-to-execute, complete, consistent, and near-optimal decision procedures. These compilation algorithms can be used to derive decision procedures for human teams solving time constrained decision problems.

Intercausal reasoning is a common inference pattern involving probabilistic dependence of causes of an observed common effect. The sign of this dependence is captured by a qualitative property called product synergy. The current definition of product synergy is insufficient for intercausal reasoning where there are additional uninstantiated causes of the common effect. We propose a new definition of product synergy and prove its adequacy for intercausal reasoning with direct and indirect evidence for the common effect. The new definition is based on a new property matrix half positive semi-definiteness, a weakened form of matrix positive semi-definiteness.

Propositional representation services such as truth maintenance systems offer powerful support for incremental, interleaved, problem-model construction and evaluation. Probabilistic inference systems, in contrast, have lagged behind in supporting this incrementality typically demanded by problem solvers. The problem, we argue, is that the basic task of probabilistic inference is typically formulated at too large a grain-size. We show how a system built around a smaller grain-size inference task can have the desired incrementality and serve as the basis for a low-level (propositional) probabilistic representation service.

In recent years the belief network has been used increasingly to model systems in Al that must perform uncertain inference. The development of efficient algorithms for probabilistic inference in belief networks has been a focus of much research in AI. Efficient algorithms for certain classes of belief networks have been developed, but the problem of reporting the uncertainty in inferred probabilities has received little attention. A system should not only be capable of reporting the values of inferred probabilities and/or the favorable choices of a decision; it should report the range of possible error in the inferred probabilities and/or choices. Two methods have been developed and implemented for determining the variance in inferred probabilities in belief networks. These methods, the Approximate Propagation Method and the Monte Carlo Integration Method are discussed and compared in this paper.

We describe the integration of logical and uncertain reasoning methods to identify the likely source and location of software problems. To date, software engineers have had few tools for identifying the sources of error in complex software packages. We describe a method for diagnosing software problems through combining logical and uncertain reasoning analyses. Our preliminary results suggest that such methods can be of value in directing the attention of software engineers to paths of an algorithm that have the highest likelihood of harboring a programming error.

Numerous methods for probabilistic reasoning in large, complex belief or decision networks are currently being developed. There has been little research on automating the dynamic, incremental construction of decision models. A uniform value-driven method of decision model construction is proposed for the hierarchical complete diagnosis. Hierarchical complete diagnostic reasoning is formulated as a stochastic process and modeled using influence diagrams. Given observations, this method creates decision models in order to obtain the best actions sequentially for locating and repairing a fault at minimum cost. This method construct decision models incrementally, interleaving probe actions with model construction and evaluation. The method treats meta-level and baselevel tasks uniformly. That is, the method takes a decision-theoretic look at the control of search in causal pathways and structural hierarchies.

This paper addresses learning stochastic rules especially on an inter-attribute relation based on a Minimum Description Length (MDL) principle with a finite number of examples, assuming an application to the design of intelligent relational database systems. The stochastic rule in this paper consists of a model giving the structure like the dependencies of a Bayesian Belief Network (BBN) and some stochastic parameters each indicating a conditional probability of an attribute value given the state determined by the other attributes' values in the same record. Especially, we propose the extended version of the algorithm of Chow and Liu in that our learning algorithm selects the model in the range where the dependencies among the attributes are represented by some general plural number of trees.

Previous algorithms for the construction of Bayesian belief network structures from data have been either highly dependent on conditional independence (CI) tests, or have required an ordering on the nodes to be supplied by the user. We present an algorithm that integrates these two approaches - CI tests are used to generate an ordering on the nodes from the database which is then used to recover the underlying Bayesian network structure using a non CI based method. Results of preliminary evaluation of the algorithm on two networks (ALARM and LED) are presented. We also discuss some algorithm performance issues and open problems.