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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.
Upper and lower probability inferences based on a sample from a finite univariate population
Arthur P. Dempster · 1967
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Theory of Probability
Bruno de Finetti · 1974
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A Mathematical Theory of Evidence
Glenn Shafer · 1976
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On random sets and belief functions
Hung T. Nguyen · 1978
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Fuzzy sets as a basis for a theory of possibility
Lotfi A. Zadeh · 1978
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The enterprise of knowledge: An essay on knowledge, credal probability, and chance
Isaac Levi · 1980
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Entropy and specificity in a mathematical theory of evidence
Ronald R. Yager · 1983
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Stochastic relaxation, gibbs distributions, and the bayesian restoration of images
Stuart Geman and Donald Geman · 1984
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Plausibility Measures — A General Framework for Possibility and Fuzzy Probability Measures
Ulrich Höhle and Erich Peter Klement · 1984
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A note on measures of specificity for fuzzy sets
Didier Dubois and Henri Prade · 1985
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On entropy of random sets and possibility distributions
Hung T. Nguyen · 1985
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A set-theoretic view of belief functions Logical operations and approximations by fuzzy sets
Didier Dubois and Henri Prade · 1986
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Bayes’ theorem generalized for belief functions
Philippe Smets · 1986
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Bayesian and non-Bayesian evidential updating
Henry E. Kyburg · 1987
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Some characterization of lower probabilities and other monotone capacities through the use of Möebius inversion
A. Chateauneuf and Jean-Yves Jaffray · 1989
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Consonant approximations of belief functions
Didier Dubois and Henri Prade · 1990
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Uncertainty in dempster-shafer theory: A critical re-examination
GEORGE KLIR and Arthur Ramer · 1990
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Bayesian back-propagation
Wray L. Buntine and Andreas S. Weigend · 1991
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The transferable belief model and other interpretations of Dempster–Shafer’s model
Philippe Smets · 1991
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Statistical Reasoning with Imprecise Probabilities
Peter Walley · 1991
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A Practical Bayesian Framework for Backpropagation Networks
David J. C. MacKay · 1992
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Bayesian learning via stochastic dynamics
Radford Neal · 1992
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Methods of combining multiple classifiers and their applications to handwriting recognition
L. Xu, A. Krzyzak, and C.Y. Suen · 1992
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Keeping the neural networks simple by minimizing the description length of the weights
Geoffrey E. Hinton and Drew van Camp · 1993
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Combining the results of several neural network classifiers
Galina Rogova · 1994
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A k-nearest neighbor classification rule based on dempster-shafer theory
Thierry Denœux · 1995
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Evidential reasoning approach to multisource-data classification in remote sensing
Hakil Kim and Philip H. Swain · 1995
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Bayesian learning for neural networks
Radford M. Neal · 1995
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Belief Functions and Random Sets
Hung Nguyen and Tonghui Wang · 1997
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Choquet integrals and natural extensions of lower probabilities
Zhenyuan Wang and George J. Klir · 1997
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Ensemble learning in bayesian neural networks
David Barber and Charles M. Bishop · 1998
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Learning by transduction
A. Gammerman, V. Vovk, and V. Vapnik · 1998
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Interaction transform of set functions over a finite set
Dieter Denneberg and Michel Grabisch · 1999
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An introduction to variational methods for graphical models
Michael I Jordan, Zoubin Ghahramani, Tommi S Jaakkola, and Lawrence K Saul · 1999
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Transduction with confidence and credibility
Craig Saunders, Alexander Gammerman, and Vladimir Vovk · 1999
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A neural network classifier based on dempster-shafer theory
T. Denoeux · 2000
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Classification with belief decision trees
Zied Elouedi, Khaled Mellouli, and Philippe Smets · 2000
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Decision trees using the belief function theory
Zied Elouedi, Khaled Mellouli, and Philippe Smets · 2000
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Credal sets approximation by lower probabilities: Application to credal networks
Alessandro Antonucci and Fabio Cuzzolin · 2010
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Credal semantics of Bayesian transformations in terms of probability intervals
Fabio Cuzzolin · 2010
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Support vector regression of membership functions and belief functions – Application for pattern recognition
Hicham Laanaya, Arnaud Martin, Driss Aboutajdine, and Ali Khenchaf · 2010
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Practical variational inference for neural networks
Alex Graves · 2011
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Classification systems based on rough sets under the belief function framework
Salsabil Trabelsi, Zied Elouedi, and Pawan Lingras · 2011
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Belief C-means: An extension of fuzzy C-means algorithm in belief functions framework
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Towards a unified theory of imprecise probability
Peter Walley · 2000
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A new distance between two bodies of evidence
Anne-Laure Jousselme, Dominic Grenier, and Eloi Bossé · 2001
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Ridge regression confidence machine
Ilia Nouretdinov, Tom Melluish, and Volodya Vovk · 2001
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Probability and Finance: It’s Only a Game!
Glenn Shafer and Vladimir Vovk · 2001
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Inductive confidence machines for regression
Harris Papadopoulos, Kostas Proedrou, Volodya Vovk, and Alex Gammerman · 2002
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Qualified prediction for large data sets in the case of pattern recognition
Harris Papadopoulos, Vladimir Vovk, and Alexander Gammerman · 2002
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Zhun ga Liu, Jean Dezert, Grégoire Mercier, and Quan Pan · 2012
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Combination of multiple diverse classifiers using belief functions for handling data with imperfect labels
Mahdi Tabassian, Reza Ghaderi, and Reza Ebrahimpour · 2012
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Cross-conformal predictors
Vladimir Vovk · 2012
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Venn-abers predictors, 2012
Vladimir Vovk and Ivan Petej · 2012
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Learning from the wisdom of crowds by minimax entropy
Dengyong Zhou, Sumit Basu, Yi Mao, and John Platt · 2012
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Active learning: A survey
Charu C Aggarwal, Xiangnan Kong, Quanquan Gu, Jiawei Han, and S Yu Philip · 2014
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Conformal prediction for reliable machine learning: theory, adaptations and applications
Vineeth Balasubramanian, Shen-Shyang Ho, and Vladimir Vovk · 2014
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Bayesian convolutional neural networks with bernoulli approximate variational inference, 2015
Yarin Gal and Zoubin Ghahramani · 2015
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The limitations of deep learning in adversarial settings
Nicolas Papernot, Patrick McDaniel, Somesh Jha, Matt Fredrikson, Z Berkay Celik, and Ananthram Swami · 2016
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A random forest approach using imprecise probabilities
Joaquín Abellán, Carlos Javier Mantas, and Francisco Javier García Castellano · 2017
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The multilabel naive credal classifier
Alessandro Antonucci and Giorgio Corani · 2017
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Selective classification for deep neural networks
Yonatan Geifman and Ran El-Yaniv · 2017
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Reasoning About Uncertainty
Joseph Y. Halpern · 2017
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What uncertainties do we need in bayesian deep learning for computer vision?
Alex Kendall and Yarin Gal · 2017
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A belief-theoretical approach to example-based pose estimation
Wenjuan Gong and Fabio Cuzzolin · 2018
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A new definition of entropy of belief functions in the dempster–shafer theory
Radim Jiroušek and Prakash P. Shenoy · 2018
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Reliable multi-class classification based on pairwise epistemic and aleatoric uncertainty
Vu-Linh Nguyen, Sébastien Destercke, Marie-Hélène Masson, and Eyke Hüllermeier · 2018
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Evidential deep learning to quantify classification uncertainty
Murat Sensoy, Lance Kaplan, and Melih Kandemir · 2018
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Efficient set-valued prediction in multi-class classification, 2019
Thomas Mortier, Marek Wydmuch, Krzysztof Dembczyński, Eyke Hüllermeier, and Willem Waegeman · 2019
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A meta-analysis of overfitting in machine learning
Rebecca Roelofs, Vaishaal Shankar, Benjamin Recht, Sara Fridovich-Keil, Moritz Hardt, John Miller, and Ludwig Schmidt · 2019
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The Geometry of Uncertainty: The Geometry of Imprecise Probabilities
Fabio Cuzzolin · 2020
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Hands-on bayesian neural networks - a tutorial for deep learning users
Laurent Valentin Jospin, Wray L. Buntine, Farid Boussaïd, Hamid Laga, and Mohammed Bennamoun · 2020
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Model adaptation: Unsupervised domain adaptation without source data
Rui Li, Qianfen Jiao, Wenming Cao, Hau-San Wong, and Si Wu · 2020
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An imprecise deep forest for classification
Lev V. Utkin · 2020
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Aleatoric and epistemic uncertainty in machine learning: An introduction to concepts and methods
Eyke Hüllermeier and Willem Waegeman · 2021
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An evidential classifier based on dempster-shafer theory and deep learning
Zheng Tong, Philippe Xu, and Thierry Denoeux · 2021
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Evaluating adversarial attacks on driving safety in vision-based autonomous vehicles
Jindi Zhang, Yang Lou, Jianping Wang, Kui Wu, Kejie Lu, and Xiaohua Jia · 2022
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