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Ordered valuation algebras: a generic framework for approximating inference
 International Journal of Approximate Reasoning
, 2004
"... The paper presents a generic approach of approximating inference. The method is based on the concept of valuation algebras with its wide range of possible applications in many different domains. We present convenient resourcebounded anytime algorithms, where the maximal time of computation is deter ..."
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The paper presents a generic approach of approximating inference. The method is based on the concept of valuation algebras with its wide range of possible applications in many different domains. We present convenient resourcebounded anytime algorithms, where the maximal time of computation is determined by the user. Key words: Approximation, anytime algorithms, resourcebounded computation, valuation algebras, local computation, binary join trees, bucket elimination, minibuckets. 1
Geometry of Upper Probabilities
"... In this paper we adopt the geometric approach to the theory of evidence to study the geometric counterparts of the plausibility functions, or upper probabilities. ..."
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Cited by 18 (16 self)
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In this paper we adopt the geometric approach to the theory of evidence to study the geometric counterparts of the plausibility functions, or upper probabilities.
Implementing Belief Function Computations
 International Journal of Intelligent Systems
, 2003
"... This article discusses several implementation aspects for DempsterShafer belief functions. The main objective is to propose an appropriate representation of mass functions and efficient data structures and algorithms for the two basic operations of combination and marginalization. © 2003 Wiley Peri ..."
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Cited by 17 (3 self)
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This article discusses several implementation aspects for DempsterShafer belief functions. The main objective is to propose an appropriate representation of mass functions and efficient data structures and algorithms for the two basic operations of combination and marginalization. © 2003 Wiley Periodicals, Inc. 1.
Dempster's rule for evidence ordered in a complete directed acyclic graph
 International Journal of Approximate Reasoning
, 1993
"... For the case of evidence ordered in a complete directed acyclic graph this paper presents a new algorithm with lower computational complexity for Dempster's rule than that of stepbystep application of Dempster's rule. In this problem, every original pair of evidences, has a corresponding ..."
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Cited by 15 (7 self)
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For the case of evidence ordered in a complete directed acyclic graph this paper presents a new algorithm with lower computational complexity for Dempster's rule than that of stepbystep application of Dempster's rule. In this problem, every original pair of evidences, has a corresponding evidence against the simultaneous belief in both propositions. In this case, it is uncertain whether the propositions of any two evidences are in logical conflict. The original evidences are associated with the vertices and the additional evidences are associated with the edges. The original evidences are ordered, i.e., for every pair of evidences it is determinable which of the two evidences is the earlier one. We are interested in finding the most probable completely specified path through the graph, where transitions are possible only from lower to higherranked vertices. The path is here a representation for a sequence of states, for instance a sequence of snapshots of a physical object's track. A completely specified path means that the path includes no other vertices than those stated in the path representation, as opposed to an incompletely specified path that may also include other vertices than those stated. In a hierarchical network of all subsets of the frame, i.e., of all incompletely specified paths, the original and additional evidences support subsets that are not disjoint, thus it is not possible to prune the network to a tree. Instead of propagating belief, the new algorithm reasons about the logical conditions of a completely specified path through the graph. The new algorithm is O(Θ log Θ), compared to O(Θ^log Θ) of the classic brute force algorithm. After a detailed presentation of the reasoning behind the new algorithm we conclude that it is feasible to reason without approximation about completely specified paths through a complete directed acyclic graph.
Approximations for Decision Making in the DempsterShafer Theory of Evidence
 In Uncertainty in Artificial Intelligence
, 1996
"... The computational complexity of reasoning within the DempsterShafer 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 ..."
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Cited by 12 (0 self)
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The computational complexity of reasoning within the DempsterShafer 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. 1 Introduction The complexity of the computations that have to be carried out in the DempsterShafer theory of evidence (DST) [Dempster, 1967; Shafer, 1976] is one of the main points of criticism this formalism has to face. In fact, [Orponen, 1990] shows that the combination of two basic probability assignments (bpa's) using Dempste...
Semantics of the relative belief of singletons
 International Workshop on Uncertainty and Logic UNCLOG’08
, 2008
"... Summary. In this paper we introduce the relative belief of singletons as a novel Bayesian approximation of a belief function. We discuss its nature in terms of degrees of belief under several different angles, and its applicability to different classes of belief functions. ..."
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Summary. In this paper we introduce the relative belief of singletons as a novel Bayesian approximation of a belief function. We discuss its nature in terms of degrees of belief under several different angles, and its applicability to different classes of belief functions.
Using dempstershafer theory of evidence for situation inference
 in Proceedings of the 4th European conference on Smart Sensing and Context
, 2009
"... Abstract. In the domain of ubiquitous computing, the ability to identify the occurrence of situations is a core function of being ’contextaware’. Given the uncertain nature of sensor information and inference rules, reasoning techniques that cater for uncertainty hold promise for enabling the infere ..."
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Abstract. In the domain of ubiquitous computing, the ability to identify the occurrence of situations is a core function of being ’contextaware’. Given the uncertain nature of sensor information and inference rules, reasoning techniques that cater for uncertainty hold promise for enabling the inference process. In our work, we apply the Dempster Shafer theory of evidence to infer situation occurrence with minimal use of training data. We describe a set of evidential operations for sensor mass functions using context quality and evidence accumulation for continuous situation detection. We demonstrate how our approach enables situation inference with uncertain information using a case study based on a published smart home activity data set. 1
Inner And Outer Approximation Of Belief Structures Using A Hierarchical Clustering Approach
, 2001
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