In this paper we propose a family of algorithms combining tree-clustering with conditioning that trade space for time. Such algorithms are useful for reasoning in probabilistic and deterministic networks as well as for accomplishing optimization tasks. By analyzing the problem structure it will be possible to select from a spectrum the algorithm that best meets a given time-space specification.

Probabilistic inference algorithms for finding the most probable explanation, the maximum aposteriori hypothesis, and the maximum expected utility and for updating belief are reformulated as an elimination--type algorithm called bucket elimination. This emphasizes the principle common to many of the algorithms appearing in that literature and clarifies their relationship to nonserial dynamic programming algorithms. We also present a general way of combining conditioning and elimination within this framework. Bounds on complexity are given for all the algorithms as a function of the problem's structure.

Real-time Decision algorithms are a class of incremental resource-bounded [Horvitz, 89] or anytime [Dean, 93] algorithms for evaluating influence diagrams. We present a test domain for real-time decision algorithms, and the results of experiments with several Real-time Decision Algorithms in this domain. The results demonstrate high performance for two algorithms, a decision-evaluation variant of Incremental Probabilisitic Inference [D'Ambrosio, 93] and a variant of an algorithm suggested by Goldszmidt, [Goldszmidt, 95], PKreduced. We discuss the implications of these experimental results and explore the broader applicability of these algorithms.

It is shown that the ability of the interval probability representation to capture epistemological independence is severely limited. Two events are epistemologically independent if knowledge of the first event does not alter belief (i.e., probability bounds) about the second. However, independence in this form can only exist in a 2-monotone probability function in degenerate cases i.e., if the prior bounds are either point probabilities or entirely vacuous. Additional limitations are characterized for other classes of lower probabilities as well. It is argued that these phenomena are simply a matter of interpretation. They appear to be limitations when one interprets probability bounds as a measure of epistemological indeterminacy (i.e., uncertainty arising from a lack of knowledge), but are exactly as one would expect when probability intervals are interpreted as representations of ontological indeterminacy (indeterminacy introduced by structural approximations). The ontological interpretation is introduced and discussed.

Decision analysis (DA) and the rich set of tools developed by researchers in decision making under uncertainty show great potential to penetrate the technological content of the products and services delivered by firms in a variety of industries as well as the business processes used to deliver those products and services to market. In this paper I describe work in progress at Sun Microsystems in the application of decision-analytic methods to Operational Decision Making (ODM) in its World-Wide Operations (WWOPS) Business Management Group. Working with membersof product engineering, marketing, and sales, operations planners from WWOPS have begun to use a decision-analytic framework called SCRAM (Supply Communication/Risk Assessment and Management) to structure and solve problems in product planning, tracking, and transition. Concepts such as information value provide a powerful method of managing huge information sets and thereby enable managers to focus attention on factors that matter most for their business. Finally, our process-oriented introduction of decision-analytic methods to Sun managers has led to a focused effort to develop decision support software based on methods from decision making under uncertainty.

The paper presents an efficient method for simulating the tails of a target variable Z=h(X) which depends on a set of basic variables X=(X_1, ..., X_n). To this aim, variables X_i, i=1, ..., n are sequentially simulated in such a manner that Z=h(x_1, ..., x_i-1, X_i, ..., X_n) is guaranteed to be in the tail of Z. When this method is difficult to apply, an alternative method is proposed, which leads to a low rejection proportion of sample values, when compared with the Monte Carlo method. Both methods are shown to be very useful to perform a sensitivity analysis of Bayesian networks, when very large confidence intervals for the marginal/conditional probabilities are required, as in reliability or risk analysis. The methods are shown to behave best when all scores coincide. The required modifications for this to occur are discussed. The methods are illustrated with several examples and one example of application to a real case is used to illustrate the whole process.

Bayesian networks provide a language for qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms. It is well-known, however, that there are certain independencies that we cannot capture qualitatively within the Bayesian network structure: independencies that hold only in certain contexts, i.e., given a specific assignment of values to certain variables. In this paper, we propose a formal notion of context-specific independence (CSI), based on regularities in the conditional probability tables (CPTs) at a node. We present a technique, analogous to (and based on) d-separation, for determining when such independence holds in a given network. We then focus on a particular qualitative representation scheme - tree-structured CPTs - for capturing CSI. We suggest ways in which this representation can be used to support effective inference algorithms. In particular, we present a structural decomposition of the resulting network which can improve the performance of clustering algorithms, and an alternative algorithm based on cutset conditioning.

An algorithm is developed for finding a close to optimal junction tree of a given graph G. The algorithm has a worst case complexity O(c^k n^a) where a and c are constants, n is the number of vertices, and k is the size of the largest clique in a junction tree of G in which this size is minimized. The algorithm guarantees that the logarithm of the size of the state space of the heaviest clique in the junction tree produced is less than a constant factor off the optimal value. When k = O(log n), our algorithm yields a polynomial inference algorithm for Bayesian networks.

The computational complexity of reasoning within the Dempster-Shafer theory of evidence is one of the main points of criticism this formalism has to face. To overcome this difficulty various approximation algorithms have been suggested that aim at reducing the number of focal elements in the belief functions involved. Besides introducing a new algorithm using this method, this paper describes an empirical study that examines the appropriateness of these approximation procedures in decision making situations. It presents the empirical findings and discusses the various tradeoffs that have to be taken into account when actually applying one of these methods.

This paper deals with a scene recognition system in a robotics contex. The general problem is to match images with a priori descriptions. A typical mission would consist in identifying an object in an installation with a vision system situated at the end of a manipulator and with a human operator provided description, formulated in a pseudo-natural language, and possibly redundant. The originality of this work comes from the nature of the description, from the special attention given to the management of imprecision and uncertainty in the interpretation process and from the way to assess the description redundancy so as to reinforce the overall matching likelihood.