Related papers: Hierarchical Evidence and Belief Functions
Within the framework of evidence theory, the confidence functions of different information can be combined into a combined confidence function to solve uncertain problems. The Dempster combination rule is a classic method of fusing…
We introduce a new logic of graded distributed belief that allows us to express the fact that a group of agents distributively believe that a certain fact holds with at least strength k. We interpret our logic by means of computationally…
The problem of belief tracking in the presence of stochastic actions and observations is pervasive and yet computationally intractable. In this work we show however that probabilistic beliefs can be maintained in factored form exactly and…
Valuation-based system (VBS) provides a general framework for representing knowledge and drawing inferences under uncertainty. Recent studies have shown that the semantics of VBS can represent and solve Bayesian decision problems (Shenoy,…
Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through…
The belief function approach to uncertainty quantification as proposed in the Demspter-Shafer theory of evidence is established upon the general mathematical models for set-valued observations, called random sets. Set-valued predictions are…
In this chapter, we present and discuss a new generalized proportional conflict redistribution rule. The Dezert-Smarandache extension of the Demster-Shafer theory has relaunched the studies on the combination rules especially for the…
This paper investigates the issues of combination and normalization of interval-valued belief structures within the framework of Dempster-Shafer theory of evidence. Existing approaches are reviewed and thoroughly analyzed. The advantages…
Jeffrey's rule of conditioning has been proposed in order to revise a probability measure by another probability function. We generalize it within the framework of the models based on belief functions. We show that several forms of…
We propose an information-fusion approach based on belief functions to combine convolutional neural networks. In this approach, several pre-trained DS-based CNN architectures extract features from input images and convert them into mass…
Variational inference algorithms such as belief propagation have had tremendous impact on our ability to learn and use graphical models, and give many insights for developing or understanding exact and approximate inference. However,…
Shafer's belief functions were introduced in the seventies of the previous century as a mathematical tool in order to model epistemic probability. One of the reasons that they were not picked up by mainstream probability was the lack of a…
Dempster-Shafer evidence theory has been widely used in various fields of applications, because of the flexibility and effectiveness in modeling uncertainties without prior information. Besides, it has been proven that the quantum theory…
Statistical inference as a formal scientific method to covert experience to knowledge has proven to be elusively difficult. While frequentist and Bayesian methodologies have been accepted in the contemporary era as two dominant schools of…
This work studies the distributed learning process on a network of agents. Agents make partial observation about an unknown hypothesis and iteratively share their beliefs over a set of possible hypotheses with their neighbors to learn the…
Belief systems are often treated as globally consistent sets of propositions or as scalar-valued probability distributions. Such representations tend to obscure the internal structure of belief, conflate external credibility with internal…
The concept of movable evidence masses that flow from supersets to subsets as specified by experts represents a suitable framework for reasoning under uncertainty. The mass flow is controlled by specialization matrices. New evidence is…
This paper is devoted to expressiveness of hypergraphs for which uncertainty propagation by local computations via Shenoy/Shafer method applies. It is demonstrated that for this propagation method for a given joint belief distribution no…
Hierarchical task decomposition is a method used in many agent systems to organize agent knowledge. This work shows how the combination of a hierarchy and persistent assertions of knowledge can lead to difficulty in maintaining logical…
This paper is concerned with the apparent greatest weakness of the Mathematical Theory of Evidence (MTE) of Shafer \cite{Shafer:76}, which has been strongly criticized by Wasserman \cite{Wasserman:92ijar}. Weaknesses of Shafer's proposal…