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52
Resource-bounded and anytime approximation of belief function computations
- INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
, 2002
"... This papers proposes a new approximation method for Dempster-Shafer belief functions. The method is based on a new concept of incomplete belief potentials. It allows to compute simultaneously lower and upper bounds for belief and plausibility. Furthermore, it can be used for a resource-bounded propa ..."
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This papers proposes a new approximation method for Dempster-Shafer belief functions. The method is based on a new concept of incomplete belief potentials. It allows to compute simultaneously lower and upper bounds for belief and plausibility. Furthermore, it can be used for a resource-bounded propagation scheme, in which the user determines in advance the maximal time available for the computation. This leads then to convenient, interruptible anytime algorithms giving progressively better solutions as execution time goes on, thus offering to trade the quality of results against the costs of computation. The paper demonstrates the usefulness of these new methods and shows its advantages and drawbacks compared to existing techniques.
Justification of Plan Recognition Results
- In Proceedings of 12th European Conference on Artificial Intelligence (ECAI-96
, 1996
"... . Expert systems are typically expected to be able to justify their decisions to the user. This paper argues that help systems or tutoring systems based on a plan recognizer can equally benefit from an explanation component. To this end a plan recognition system equipped with a user model is present ..."
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. Expert systems are typically expected to be able to justify their decisions to the user. This paper argues that help systems or tutoring systems based on a plan recognizer can equally benefit from an explanation component. To this end a plan recognition system equipped with a user model is presented and the techniques required to generate precise and useful justifications of its results are introduced. The system answers questions about various aspects of a decision and allows its user to check and adjust the user model if necessary. 1 Introduction Knowledge-based expert systems are almost expected to possess an explanation component that provides a justification of the results of their internal reasoning processes to their users (e.g. [10, 13]). This allows a "plausibility check" of the system's decision by comparing its inference steps with the user's own domain knowledge. Such an enhanced transparency of the system behavior is meant to increase the user's acceptance of the solut...
On the Properties of the Intersection Probability
, 2007
"... In this paper, drawing inspiration from the commutativity results which hold for a number of Bayesian approximations of belief functions (like pignistic function and relative plausibility of singletons) we study the properties of a new probabilistic approximation of belief functions derived from geo ..."
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Cited by 4 (3 self)
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In this paper, drawing inspiration from the commutativity results which hold for a number of Bayesian approximations of belief functions (like pignistic function and relative plausibility of singletons) we study the properties of a new probabilistic approximation of belief functions derived from geometric methods: the intersection probability. The intersection probability inherits its name from the fact that, when combined with a Bayesian function through Dempster’s rule, it is equivalent to the intersection of the line joining a pair of belief and plausibility functions with the affine space of Bayesian pseudo belief functions. Its relation with the convex closure operator in the Cartesian space is analyzed, and equivalent conditions under which they commute are given, showing its similarity with orthogonal projection and pignistic transformation. A thorough analysis of the distance between intersection probability and pignistic function in a case study is conducted, and stringent equivalence relations in terms of mass equi-distribution inferred from it.
Representing Heuristic Knowledge in D-S Theory
- STANFORD UNIVERSITY
"... The Dempster-Shafer theory of evidence has been used intensively to deal with uncertainty in knowledge-based systems. However the representation of uncertain relationships between evidence and hypothesis groups (heuristic knowledge) is still a major research problem. This paper presents an approach ..."
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Cited by 3 (2 self)
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The Dempster-Shafer theory of evidence has been used intensively to deal with uncertainty in knowledge-based systems. However the representation of uncertain relationships between evidence and hypothesis groups (heuristic knowledge) is still a major research problem. This paper presents an approach to representing such heuristic knowledge by evidential mappings which are dened on the basis of mass functions. The relationships between evidential mappings and multivalued mappings, as well as between evidential mappings and Bayesian multi- valued causal link models in Bayesian theory are discussed. Following this the detailed procedures for constructing evidential mappings for any set of heuristic rules are introduced. Several situations of belief propagation are discussed.
Evidential reasoning in network intrusion detection systems
- Information Security and Privacy: First Australasian Conference, ACISP’96
, 1996
"... Abstract. Intrusion Detection Systems (IDS) have previously been built by hand. These systems have difficulty successfully classifying intruders, and require a significant amount of computational overhead making it difficult to create robust real-time IDS systems. Artificial Intelligence techniques ..."
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Abstract. Intrusion Detection Systems (IDS) have previously been built by hand. These systems have difficulty successfully classifying intruders, and require a significant amount of computational overhead making it difficult to create robust real-time IDS systems. Artificial Intelligence techniques can reduce the human effort required to build these systems and can improve their performance. AI has recently been used in Intrusion Detection (ID) for anomaly detection, data reduction and induction, or discovery, of rules explaining audit data [l]. This paper proposes the application of evidential reasoning for dealing with uncertainty in Intrusion Detection Systems. We show how dealing with uncertainty can allow the system to detect the abnormality in the user behavior more efficiently. 1
Approximating the Combination of Belief Functions Using the Fast Möbius Transform in a Coarsened Frame
, 2002
"... A method is proposed for reducing the size of a frame of discernment, in such a way that the loss of information content in a set of belief functions is minimized. This method may be seen as a hierarchical clustering procedure applied to the columns of a binary data matrix, using a particular dissim ..."
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Cited by 3 (2 self)
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A method is proposed for reducing the size of a frame of discernment, in such a way that the loss of information content in a set of belief functions is minimized. This method may be seen as a hierarchical clustering procedure applied to the columns of a binary data matrix, using a particular dissimilarity measure. It allows to compute approximations of the mass functions, which can be combined efficiently in the coarsened frame using the Fast Möbius Transform algorithm, yielding inner and outer approximations of the combined belief function.
Three alternative combinatorial formulations of the theory of evidence
, 2009
"... In this paper we introduce three alternative combinatorial formulations of the theory of evidence (ToE), by proving that both plausibility and commonality functions share the structure of “sum function ” with belief functions. We compute their Moebius inverses, which we call basic plausibility and c ..."
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In this paper we introduce three alternative combinatorial formulations of the theory of evidence (ToE), by proving that both plausibility and commonality functions share the structure of “sum function ” with belief functions. We compute their Moebius inverses, which we call basic plausibility and commonality assignments. As these results are achieved in the framework of the geometric approach to uncertainty measures, the equivalence of the associated formulations of the ToE is mirrored by the geometric congruence of the related simplices. We can then describe the point-wise geometry of these sum functions in terms of rigid transformations mapping them onto each other. Combination rules can be applied to plausibility and commonality functions through their Moebius inverses, leading to interesting applications of such inverses to the probabilistic transformation problem.
On the relative belief transform
, 2011
"... In this paper we discuss the semantics and properties of the relative belief transform, a probability transformation of belief functions closely related to the classical plausibility transform. We discuss its rationale in both the probability-bound and Shafer’s interpretations of belief functions. E ..."
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In this paper we discuss the semantics and properties of the relative belief transform, a probability transformation of belief functions closely related to the classical plausibility transform. We discuss its rationale in both the probability-bound and Shafer’s interpretations of belief functions. Even though the resulting probability (as it is the case for the plausibility transform) is not consistent with the original belief function, an interesting rationale in terms of optimal strategies in a non-cooperative game can be given in the probability-bound interpretation to both relative belief and plausibility of singletons. On the other hand, we prove that relative belief commutes with Dempster’s orthogonal sum, meets a number of properties which are the duals of those met by the relative plausibility of singletons, and commutes with convex closure in a similar way to Dempster’s rule. This supports the argument that relative plausibility and belief transform are indeed naturally associated with the D-S framework, and highlights a classification of probability transformations in two families, according to the operator they relate to. Finally, we point out that relative belief is only a member of a class of “relative mass” mappings, which can be interpreted as low-cost proxies for both plausibility and pignistic transforms.
Credal semantics of Bayesian transformations in terms of probability intervals
- Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on
, 2010
"... probability intervals ..."
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MOEBIUS INVERSES OF PLAUSIBILITY AND COMMONALITY FUNCTIONS AND THEIR GEOMETRIC INTERPRETATION
- INTERNATIONAL JOURNAL OF UNCERTAINTY, FUZZINESS AND KNOWLEDGE-BASED SYSTEMS
, 2007
"... In this work we extend the geometric approach to the theory of evidence in order to study the geometric behavior of the two quantities inherently associated with a belief function. i.e. the plausibility and commonality functions. After introducing the analogous of the basic probability assignment fo ..."
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Cited by 1 (1 self)
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In this work we extend the geometric approach to the theory of evidence in order to study the geometric behavior of the two quantities inherently associated with a belief function. i.e. the plausibility and commonality functions. After introducing the analogous of the basic probability assignment for plausibilities and commonalities, we exploit it to understand the simplicial form of both plausibility and commonality spaces. Given the intuition provided by the binary case we prove the congruence of belief, plausibility, and commonality spaces for both standard and unnormalized belief functions, and describe the point-wise geometry of these sum functions in terms of the rigid transformation mapping them onto each other. This leads us to conjecture that the D-S formalism may be in fact a geometric calculus in the line of geometric probability, and opens the way to a wider application of discrete mathematics to subjective probability.
