Resource bounded and anytime approximation of belief function computations

PRICAI 2008: Trends in Artificial Intelligence

2008

Abstract. In this paper we prove that a recent Bayesian approximation of belief functions, the relative belief of singletons, meets a number of properties with respect to Dempster's rule of combination which mirrors those satisfied by the relative plausibility of singletons. In particular, its operator commutes with Dempster's sum of plausibility functions, while perfectly representing a plausibility function when combined through Dempster's rule. This suggests a classification of all Bayesian approximations into two families according to the operator they relate to.

“…The orthogonal sum can be naturally extended to pseudo b.f.s by applying (5) to the Moebius inverses m ς1 , m ς2 of a pair of p.b.f.s. As Cuzzolin has proven [19] Proposition 4.…”

Section: Dempster's Sum Of Pseudo Belief Functionsmentioning

confidence: 99%

Section: Introduction: a New Bayesian Approximationmentioning

confidence: 99%

Dual Properties of the Relative Belief of Singletons

PRICAI 2008: Trends in Artificial Intelligence

2008

“…In particular, many people worked on the problem of finding a probabilistic approximation of an arbitrary belief function. Several papers [2][3][4][5][6][7][8][9][10] have been published on this issue, mainly in order to find efficient implementations of the rule of combination aiming to reduce the number of focal elements. The connection between belief functions and probabilities is as well crucial in Smets' "Transferable Belief Model" [11].…”

Section: Introductionmentioning

confidence: 99%

On the Orthogonal Projection of a Belief Function

Lecture Notes in Computer Science

2007

Abstract. In this paper we study a new probability associated with any given belief function b, i.e. the orthogonal projection π [b] of b onto the probability simplex P. We provide an interpretation of π [b] in terms of a redistribution process in which the mass of each focal element is equally distributed among its subsets, establishing an interesting analogy with the pignistic transformation. We prove that orthogonal projection commutes with convex combination just as the pignistic function does, unveiling a decomposition of π [b] as convex combination of basis pignistic functions. Finally we discuss the norm of the difference between orthogonal projection and pignistic function in the case study of a quaternary frame, as a first step towards a more comprehensive picture of their relation.

“…As probability measures or Bayesian belief functions are just a special class of b.f.s (for which m(A) = 0 when |A| > 1), the relation between beliefs and probabilities plays a major role in the theory of evidence [9,14,23,11,12,13,2]. Tessem [21], for instance, incorporated only the highest-valued focal elements in his m klx approximation; a similar approach inspired the summarization technique formulated by Lowrance et al [15].…”

Section: Previous Work On Bayesian Approximationmentioning

confidence: 99%

Semantics of the Relative Belief of Singletons

Advances in Soft Computing