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Probabilistic Transformations of Belief Functions [chapter]

Milan Daniel
2005 Lecture Notes in Computer Science  
A series of various probabilistic transformations is examined namely from the point of view of their consistency with rules for belief function combination and their consistency with probabilistic upper  ...  Alternative approaches to the widely known pignistic transformation of belief functions are presented and analyzed.  ...  Definition 4 A function PT from the set of all belief functions to the set of the Bayesian ones is called probabilistic transformation of belief functions if it satisfies: (i) p-consistency, i. e.  ... 
doi:10.1007/11518655_46 fatcat:gavbyf6frbhxlbwkdbn2kwghsm

Genetic Algorithm Based on Similarity for Probabilistic Transformation of Belief Functions $

Yilin Dong, Xinde Li, Jean Dezert, Pei Li, Xianghui Li
unpublished
each singleton in order to obtain Bayesian belief function for decision making problems.  ...  In the process of such transformation, how to precisely evaluate the clossness between original Basic Belief Assignments (BBAs) and transformed BBAs is important.  ...  Basis of belief functions In this section, we introduce the belief functions terminology of DST and the notations used in the sequel of this paper. 95 DST basis In DST [2] , the elements θ i (i =  ... 
fatcat:bzxpociuy5f37if757ns6eur4a

Evaluation of Probabilistic Transformations for Evidential Data Association [chapter]

Mohammed Boumediene, Jean Dezert
2020 Communications in Computer and Information Science  
To treat such issue, recent research focus on the evidential approach using belief functions, which are interpreted as an extension of the probabilistic model for reasoning about uncertainty.  ...  Finally, a probabilistic approximation of these combined masses is done to make-decision on associations. Several probabilistic transformations have been proposed in the literature.  ...  MultiScale Probability The Multiscale Probability (MulP ) transformation [19] highlights the proportion of each hypothesis in the frame of discernment by using a difference function between belief and  ... 
doi:10.1007/978-3-030-50143-3_24 fatcat:6lztayzr4vfdtguldea4jel6dm

Combination of Evidence with Different Weighting Factors: A Novel Probabilistic-Based Dissimilarity Measure Approach

Mengmeng Ma, Jiyao An
2015 Journal of Sensors  
Firstly, an improved probabilistic transformation function is proposed to map basic belief assignments (BBAs) to probabilities.  ...  Then, a new dissimilarity measure integrating fuzzy nearness and introduced correlation coefficient is proposed to characterize not only the difference between basic belief functions (BBAs) but also the  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2015/509385 fatcat:fgmzv5f7erh57dle4jyomuli4y

Extend Transferable Belief Models with Probabilistic Priors

Chunlai Zhou, Yuan Feng
2015 Conference on Uncertainty in Artificial Intelligence  
In this paper, we extend Smets' transferable belief model (TBM) with probabilistic priors.  ...  We extend standard Dempster models with prior probabilities to represent beliefs and distinguish between two types of induced mass functions on an extended Dempster model: one for believing and the other  ...  EXTENDED DEMPSTER MODELS In order to motivate our work of extending Smets' transferable belief models with probabilistic priors, we first represent belief functions through Dempster models. 3.1 EXTENDED  ... 
dblp:conf/uai/ZhouF15 fatcat:ze3fmltmdncgfhxsuedry5n3um

Evidential Confirmation as Transformed Probability [article]

Benjamin N. Grosof
2013 arXiv   pre-print
It recasts some of confirmation theory's advantages in terms of the psychological accessibility of probabilistic information in different (transformed) formats.  ...  We show how to represent two major such alternative approaches to evidential confirmation not only in terms of transformed (Bayesian) probability, but also in terms of each other.  ...  Thanks also to Richard Duda, Peter Hart, and Nils Nilsson for their interest, and their help in providing the unpublished history of the development of the PROSPECTOR method.  ... 
arXiv:1304.3439v1 fatcat:2md7qvuxknbkvaqvdsecgexqam

Is entropy enough to evaluate the probability transformation approach of belief function?

Deqiang Han, J Dezert, Chongzhao Han, Yi Yang
2010 2010 13th International Conference on Information Fusion  
In Dempster-Shafer Theory (DST) of evidencee and transferable belief model (TBM), the probability transformation is necessary and crucial for decision-making.  ...  The evaluation of the quality of the probability transformation is usually based on the entropy or the probabilistic information content (PIC) measures, which are questioned in this paper.  ...  Conclusion Probability transformation of belief function can be considered as a probabilistic approximation of belief assignment, which aims to gain more reliable decision results.  ... 
doi:10.1109/icif.2010.5711937 fatcat:6emcwmwynzcitp57or5o2bv2cq

Is Entropy Enough To Evaluate The Probability Transformation Approach Of Belief Function?

Deqiang Han, Jean Dezert, Chongzhao Han, Yi Yang
2015 Zenodo  
In Dempster-Shafer Theory (DST) of evidencee and transferable belief model (TBM), the probability transformation is necessary and crucial for decision-making.  ...  The evaluation of the quality of the probability transformation is usually based on the entropy or the probabilistic information content (PIC) measures, which are questioned in this paper.  ...  Conclusion Probability transformation of belief function can be considered as a probabilistic approximation of belief assignment, which aims to gain more reliable decision results.  ... 
doi:10.5281/zenodo.22562 fatcat:sttfot4sffhqdc5nqjuzae3jbi

The computational complexity of probabilistic inference using bayesian belief networks

Gregory F. Cooper
1990 Artificial Intelligence  
Bayesian belief networks provide a natural, efficient method for representing probabilistic dependencies among a set of variables.  ...  Algorithms have been developed previously for efficient probabilistic inference using special classes of belief networks.  ...  Army Research Office, and grant LM-07033 from the National Library of Medicine. Computer facilities were provided by the SUMEX-AIM resource under grant RR-00785 from the National Institutes of Health.  ... 
doi:10.1016/0004-3702(90)90060-d fatcat:gkme3lmkxja5zcojghutnq4bre

An Axiomatic Framework for Belief Updates [article]

David Heckerman
2013 arXiv   pre-print
For example, it is shown that belief updates in a probabilistic context must be equal to some monotonic transformation of a likelihood ratio.  ...  He showed that if a measure of belief satisfies several fundamental properties, then the measure must be some monotonic transformation of a probability.  ...  Acknowledgements I wish to thank Eric Horvitz for help with the development of this paper. I thank Eric Horvitz, Judea Pearl, and Peter Cheeseman for insightful discussions conceming belief updates.  ... 
arXiv:1304.3091v1 fatcat:5kvwj4r6uvdwfcvwsvi2yuowzm

Smart Transformations: The Evolution of Choice Principles [article]

Paolo Galeazzi, Michael Franke
2015 arXiv   pre-print
In other words, we will look at evolutionary competition of payoff transformations in "meta-games", obtained from averaging over payoffs of single games.  ...  Here, we want to extend this existing approach even further by asking: which general patterns of subjective conceptualizations of payoff functions are evolutionarily successful across a class of games.  ...  Through this abstract we will assume that probabilistic and non-probabilistic beliefs are just two different and compatible forms of belief.  ... 
arXiv:1505.07054v1 fatcat:dcnlgp6gevarlfzdgdwuird6fq

A New Probabilistic Transformation Based On Evolutionary Algorithm For Decision Making

Yilin Dong, Xinde Li, Jean Dezert
2017 Zenodo  
In this paper, work by us also takes inspiration from both Bayesian transformation camps, with a novel evolutionary-based probabilistic transformation (EPT) to select the qualified Bayesian belief function  ...  The study of alternative probabilistic transformation (PT) in DS theory has emerged recently as an interesting topic, especially in decision making applications.  ...  BASIS OF BELIEF FUNCTIONS In this section, we introduce the belief functions terminology of DST and the notations used in the sequel of this paper. A.  ... 
doi:10.5281/zenodo.1042028 fatcat:ux7sjoknmzaanda4k6xpaytprq

Second-Order Belief Hidden Markov Models [chapter]

Jungyeul Park, Mouna Chebbah, Siwar Jendoubi, Arnaud Martin
2014 Lecture Notes in Computer Science  
First-order probabilistic HMMs were adapted to the theory of belief functions such that Bayesian probabilities were replaced with mass functions.  ...  The probabilistic HMMs have been one of the most used techniques based on the Bayesian model.  ...  First-order probabilistic and belief HMMs and tried to apply our idea to the theory of belief functions. We extended previous works on belief HMMs to the second-order model.  ... 
doi:10.1007/978-3-319-11191-9_31 fatcat:zze6tcxfejgihe7gz37froyvxm

Belief Propagation for Probabilistic Slow Feature Analysis

Toshiaki Omori, Tomoki Sekiguchi, Masato Okada
2017 Journal of the Physical Society of Japan  
Here, we rigorously derive the marginal likelihood function of the probabilistic framework of SFA by using belief propagation.  ...  For this purpose, we rigorously derive the marginal likelihood function of probabilistic SFA by means of the belief propagation.  ...  (10) ] in belief propagation. 16, 17, 22) A joint probability density function pðx 1:t ; y t Þ can be expressed as pðx 1:t ; y t Þ ¼ pðx 1:t jy t Þpð y t Þ ¼ pðx 1:tÀ1 jy t Þpðx t jy t Þpð y t Þ ¼  ... 
doi:10.7566/jpsj.86.084802 fatcat:hx5toih2zzg6rjpf553dryzchi

Belief Hidden Markov Model for speech recognition [article]

Siwar Jendoubi
2015 arXiv   pre-print
Consequently, using the belief HMM recognizer can greatly minimize the cost of these systems.  ...  In this paper, we present a new approach for recognizing speech based on belief HMMs instead of proba-bilistic HMMs.  ...  BELIEF HMM Belief HMM is an extension of the probabilistic HMM to belief functions [7] , [6] , [8] . Like probabilistic HMM, the belief HMM is a combination of two stochastic processes.  ... 
arXiv:1501.05530v1 fatcat:cvnjohlt3nb55nwgr3bqq22pwu
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