ON THE USE OF THE DEMPSTER SHAFER MODEL IN INFORMATION INDEXING AND RETRIEVAL APPLICATIONS

The Dempster Shafer theory of evidence concerns the elicitation and manipulation of degrees of belief rendered by multiple sources of evidence to a common set of propositions. Information indexing and retrieval applications use a variety of quantitative means - both probabilistic and quasi-probabilistic - to represent and manipulate relevance numbers and index vectors. Recently, several proposals were made to use the Dempster Shafes model as a relevance calculus in such applications. The paper provides a critical review of these proposals, pointing at several theoretical caveats and suggesting ways to resolve them. The methodology is based on expounding a canonical indexing model whose relevance measures and combination mechanisms are shown to be isomorphic to Shafer's belief functions and to Dempster's rule, respectively. Hence, the paper has two objectives: (i) to describe and resolve some caveats in the way the Dempster Shafer theory is applied to information indexing and retrieval, and (ii) to provide an intuitive interpretation of the Dempster Shafer theory, as it unfolds in the simple context of a canonical indexing model.Information Systems Working Papers Serie

On ϱ in a decision-theoretic apparatus of Dempster-Shafer theory

AbstractThomas M. Strat has developed a decision-theoretic apparatus for Dempster-Shafer theory (Decision analysis using belief functions, Intern. J. Approx. Reason. 4(5/6), 391–417, 1990). In this apparatus, expected utility intervals are constructed for different choices. The choice with the highest expected utility is preferable to others. However, to find the preferred choice when the expected utility interval of one choice is included in that of another, it is necessary to interpolate a discerning point in the intervals. This is done by the parameter ϱ, defined as the probability that the ambiguity about the utility of every nonsingleton focal element will turn out as favorable as possible. If there are several different decision makers, we might sometimes be more interested in having the highest expected utility among the decision makers rather than only trying to maximize our own expected utility regardless of choices made by other decision makers. The preference of each choice is then determined by the probability of yielding the highest expected utility. This probability is equal to the maximal interval length of ϱ under which an alternative is preferred. We must here take into account not only the choices already made by other decision makers but also the rational choices we can assume to be made by later decision makers. In Strats apparatus, an assumption, unwarranted by the evidence at hand, has to be made about the value of ϱ. We demonstrate that no such assumption is necessary. It is sufficient to assume a uniform probability distribution for ϱ to be able to discern the most preferable choice. We discuss when this approach is justifiable

Local Computation in Hypertrees

This is an unpublished monograph that was widely distributed (and cited). It was first written in August 1988 and subseqently revised.The monograph describes theory and algorithms for computation of marginals using local computation that applies to a large number of domains including probability theory, Dempster-Shafer theory of belief functions, discrete optimization, and constraint satisfaction.Research described in this monograph was funded by NSF grant IST-8610293, and three grants from KPMG Peat Marwick Foundation's Research Opportunities in Auditing program

Influence diagrams : a new approach to modelling games

Game theory seeks to describe the interaction of two or more actors with distinct objectives. This is achieved using a mathematical model known as a game. Virtually all game theory relies on either the extensive form or the normal form to represent the games being studied. By drawing on the previously unrelated fields of game theory and graphical modelling, and by taking a new approach to the way in which a game is modelled, an alternative to the extensive and normal forms is developed: the belief influence diagram (BID). Starting from the basic definition of a game and using a new form of conditional belief called a prospective function, it is shown how the decision influence diagram can be adapted to model games. The advantages of the BID over the extensive and normal forms are explored, particularly its ability to model some of the qualitative aspects of games and to model games of greater complexity. By using BIDs in the modelling of games, fresh insight can be gained into certain features of the game, such as what sources of information an actor in the game should take account of. New concepts of sufficiency and parsimony are defined which relate to the BID. It is shown how these concepts, when combined with different forms of rationality, can lead to a variety of methods for simplifying a BID, and hence simplifying the game which it represents. It is shown that such simplifications arc invariant with respect to the order in which the simplifying steps are carried out. A schematic version of the BID is used to model finite repeated games and to develop concepts of learning and local sufficiency. It is shown how BIDs can be used to facilitate an induction proof in a finite repeated game and to model a highly complex competitive market. This last example is used to illustrate how BIDs can be helpful in evaluating some qualitative aspects of a model

Dempster-Shafer Τheory Application in Recommender Systems and Comparison of Constraint Programming’s and Möbius Transform’s Implementations

Στην πτυχιακή εργασία αυτή μας απασχολεί το θέμα του Χειρισμού Αβεβαιότητας στον τομέα της Αναπαράστασης Γνώσης χρησιμοποιώντας τη θεωρία των Dempster-Shafer. Σκοπός μας είναι να μελετήσουμε μια εφαρμογή της θεωρίας σε Συστήματα Συστάσεων και να μετρήσουμε την απόδοση του κανόνα του Dempster και του υπολογισμού εμπιστοσύνης χρησιμοποιώντας μια υλοποίηση της θεωρίας βασισμένη στον Λογικό Προγραμματισμό με Περιορισμούς. Ακόμη, επιθυμούμε να συγκρίνουμε την απόδοση της υλοποίησης βασισμένη στον Λογικό Προγραμματισμό με Περιορισμούς σε τυχαίες περιπτώσεις δοκιμής με μια υλοποίηση που χρησιμοποιεί μετασχηματισμούς Möbius. Σε γενικά πλαίσια ο υπολογιστικός χρόνος για την εφαρμογή υπήρξε λογικός. Όσον αφορά τη σύγκριση, και οι δύο περιπτώσεις είχαν θετικά και αρνητικά.In this thesis, we deal with the subject of Handling Uncertainty in the field of Knowledge Representation using Dempster-Shafer theory. Our goal is to study an application of Dempster-Shafer theory to Recommended Systems and measure the performance of Dempster's rule and belief computation when using an implementation that utilizes Constraint Logic Programming (CLP). Also, we aim to compare the performance of the CLP implementation on random test cases to the performance of an implementation of Dempster-Shafer theory using Möbius Transforms. In general, the computational time for the application was rational. Regarding the comparison, each implementations has its pros and cons

A probabilistic reasoning and learning system based on Bayesian belief networks

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