@article{einstein,
author =       "Albert Einstein",
title =        "{Zur Elektrodynamik bewegter Körper}",
journal =      "Annalen der Physik",
volume =       "322",
number =       "10",
pages =        "891--921",
year =         "1905"}

@book{latexcompanion,
author    = "Michel Goossens and Frank Mittelbach and Alexander Samarin",
title     = "The \LaTeX\ Companion",
year      = "1993",
publisher = "Addison-Wesley"}

@inproceedings{langley00,
 author    = {P. Langley},
 title     = {Crafting Papers on Machine Learning},
 year      = {2000},
 pages     = {1207--1216},
 editor    = {Pat Langley},
 booktitle     = {Proceedings of the 17th International Conference
              on Machine Learning (ICML 2000)},
 address   = {Stanford, CA},
 publisher = {Morgan Kaufmann}
}

@TechReport{mitchell80,
  author = 	 "T. M. Mitchell",
  title = 	 "The Need for Biases in Learning Generalizations",
  institution =  "Computer Science Department, Rutgers University",
  year = 	 "1980",
  address =	 "New Brunswick, MA",
}

@phdthesis{kearns89,
  author = {M. J. Kearns},
  title =  {Computational Complexity of Machine Learning},
  school = {Department of Computer Science, Harvard University},
  year =   {1989}
}

@Book{MachineLearningI,
  editor = 	 "R. S. Michalski and J. G. Carbonell and T.
		  M. Mitchell",
  title = 	 "Machine Learning: An Artificial Intelligence
		  Approach, Vol. I",
  publisher = 	 "Tioga",
  year = 	 "1983",
  address =	 "Palo Alto, CA"
}

@Book{DudaHart2nd,
  author =       "R. O. Duda and P. E. Hart and D. G. Stork",
  title =        "Pattern Classification",
  publisher =    "John Wiley and Sons",
  edition =      "2nd",
  year =         "2000"
}

@misc{anonymous,
  title= {Suppressed for Anonymity},
  author= {Author, N. N.},
  year= {2021}
}

@InCollection{Newell81,
  author =       "A. Newell and P. S. Rosenbloom",
  title =        "Mechanisms of Skill Acquisition and the Law of
                  Practice", 
  booktitle =    "Cognitive Skills and Their Acquisition",
  pages =        "1--51",
  publisher =    "Lawrence Erlbaum Associates, Inc.",
  year =         "1981",
  editor =       "J. R. Anderson",
  chapter =      "1",
  address =      "Hillsdale, NJ"
}


@Article{Samuel59,
  author = 	 "A. L. Samuel",
  title = 	 "Some Studies in Machine Learning Using the Game of
		  Checkers",
  journal =	 "IBM Journal of Research and Development",
  year =	 "1959",
  volume =	 "3",
  number =	 "3",
  pages =	 "211--229"
}

@book{popper2014conjectures,
	title={Conjectures and refutations: The growth of scientific knowledge},
	author={Popper, Karl},
	year={2014},
	publisher={Routledge}
}


@Inproceedings{Bottou2013,
	author={Bottou, L{\'e}on},
	editor={Sch{\"o}lkopf, Bernhard
	and Luo, Zhiyuan
	and Vovk, Vladimir},
	title={In Hindsight: Doklady Akademii Nauk {SSSR}, 181(4), 1968},
	bookTitle={Empirical Inference: Festschrift in Honor of Vladimir N. Vapnik},
	year={2013},
	publisher={Springer},
	optaddress={Berlin, Heidelberg},
	pages={3--5},
	abstract={This short contribution presents the first paper in which Vapnik and Chervonenkis describe the foundations of Statistical Learning Theory (Vapnik, Chervonenkis (1968) Proc USSR Acad Sci 181(4): 781--783).},
	optisbn={978-3-642-41136-6},
	optdoi={10.1007/978-3-642-41136-6_1},
	opturl={https://doi.org/10.1007/978-3-642-41136-6_1}
}


@incollection{berger,
	author = {Berger, James O.},
	booktitle = {Robustness of Bayesian Analyses},
	date-added = {2020-02-09 20:43:03 +0000},
	date-modified = {2020-02-09 20:48:05 +0000},
	editor = {Kadane, Joseph B.},
	publisher = {Amsterdam : North-Holland},
	title = {The robust {B}ayesian viewpoint},
	year = {1984}}



 @article{pajor,
 author = {Keith Ball and Alain Pajor},
 journal = {Proceedings of the American Mathematical Society},
 number = {1},
 pages = {225--231},
 publisher = {American Mathematical Society},
 title = {Convex Bodies with Few Faces},
 volume = {110},
 year = {1990}
}



@inproceedings{mosler,
author={Mosler, Karl},
title={Zonoids and lift zonoids},
booktitle={Multivariate Dispersion, Central Regions, and Depth: The Lift Zonoid Approach},
year={2002},
publisher={New York : Springer},
series = {Lecture Notes in Statistics},
volume={165},
pages={25--78}
}

@article{shelah1972combinatorial,
	title={A combinatorial problem; stability and order for models and theories in infinitary languages},
	author={Shelah, Saharon},
	journal={Pacific Journal of Mathematics},
	volume={41},
	number={1},
	pages={247--261},
	year={1972},
	publisher={Mathematical Sciences Publishers}
}



@InProceedings{eyke_new,
  title = 	 {Quantification of Credal Uncertainty in Machine Learning: A Critical Analysis and Empirical Comparison},
  author =       {H\"ullermeier, Eyke and Destercke, S\'ebastien and Shaker, Mohammad Hossein},
  booktitle = 	 {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence},
  pages = 	 {548--557},
  year = 	 {2022},
  editor = 	 {Cussens, James and Zhang, Kun},
  volume = 	 {180},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {01--05 Aug},
  publisher =    {PMLR}
}

@article{abellan3,
title = {Additivity of uncertainty measures on credal sets},
journal = {International Journal of General Systems},
volume = {34},
number = {6},
pages = {691--713},
year = {2005},
author = {Joaquín Abellán and George J. Klir}
}


@article{jiro,
title = {A new definition of entropy of belief functions in the {D}empster–{S}hafer theory},
journal = {International Journal of Approximate Reasoning},
volume = {92},
pages = {49--65},
year = {2018},
author = {Radim Jiroušek and Prakash P. Shenoy}
}

@inproceedings{couso,
author = {Couso, Inés and Moral, Serafín and Walley, Peter},
booktitle={Proceedings of the First International Symposium on Imprecise Probabilities and Their Applications (ISIPTA 1999)},
year = {1999},
pages = {121--130},
title = {Examples of Independence for Imprecise Probabilities}
}

@book{walley,
	author = {Peter Walley},
	date-added = {2020-02-12 18:59:20 +0000},
	date-modified = {2020-02-12 19:01:33 +0000},
	publisher = {London : Chapman and Hall},
	series = {Monographs on Statistics and Applied Probability},
	title = {{Statistical Reasoning with Imprecise Probabilities}},
	volume = {42},
	year = {1991}}




 @article{cozman,
	author = {Fabio Gagliardi Cozman},
	journal = {Artificial Intelligence},
	pages = {199--233},
	title = {Credal Networks},
	volume = {120},
	year = {2000}}




 @book{levi2,
	author = {Isaac Levi},
	date-added = {2020-02-12 20:36:11 +0000},
	date-modified = {2020-02-12 20:39:21 +0000},
	publisher = {London : MIT Press},
	title = {The Enterprise of Knowledge},
	year = {1980}}	

@article{lim2,
	author = {Yuhang Cai and Lek-Heng Lim},
	journal = {{IEEE} Transactions on Information Theory},
	volume = {},
	title = {Distances between probability distributions of different dimensions},
	pages={},
	year = {2022}}




 @ARTICLE{caprio,  
 author={Caprio, Michele},  
 journal={{IEEE} Access},   
 title={Refined {P}insker’s and Reverse {P}insker’s Inequalities for Probability Distributions of Different Dimensions},   
 year={2022},  
 volume={10}, 
 number={},  
 pages={116425-116431}
 }






@article{Sauer1972density,
	title = "On the density of families of sets",
	journal = "Journal of Combinatorial Theory, Series A",
	volume = "13",
	number = "1",
	pages = "145 - 147",
	year = "1972",
	issn = "0097-3165",
	doi = "https://doi.org/10.1016/0097-3165(72)90019-2",
	url = "http://www.sciencedirect.com/science/article/pii/0097316572900192",
	author = "N Sauer",
	abstract = "If T is a family of sets and A some set we denote by T ∩ A the following family of subsets of A: T ∩ A = {F ∩ A; FϵT}. P. Erdös (oral communication) transmitted to me in Nice the following question: Is it true that if T is a family of subsets of some infinite set S then either there exists to each number n a set A ⊂ S with |A| = n such that |T ∩ A| = 2n or there exists some number N such that |T ∩ A| ⩽ |A|c for each A ⊂ S with |A| ⩾ N and some constant c? In this paper we will answer this question in the affirmative by determining the exact upper bound. (Theorem 2).1"
}
@book{pajor1985sous,
	title={Sous-espaces LN/L des espaces de Banach},
	author={Pajor, Alain},
	number={16},
	year={1985},
	publisher={Hermann}
}

@book{Vapnik2006b,
	author = {Vapnik, Vladimir N.},
	year = {2006},
	title = {{Estimation of dependences based on empirical data. Empirical inference science: Afterword of 2006 / Vladimir Vapnik}},
	address = {New York, NY and [Heidelberg]},
	publisher = {Springer},
	isbn = {0387308652}
}





@article{serfling1974probability,
	title={Probability inequalities for the sum in sampling without replacement},
	author={Serfling, Robert J},
	journal={The Annals of Statistics},
	pages={39--48},
	year={1974},
	publisher={JSTOR}
}


@book{vapnik2013nature,
	title={The nature of statistical learning theory},
	author={Vapnik, Vladimir},
	year={2013},
	publisher={Springer science \& business media}
}


@article{massart1990tight,
	title={The tight constant in the {D}voretzky-{K}iefer-{W}olfowitz inequality},
	author={Massart, Pascal},
	journal={The annals of Probability},
	pages={1269--1283},
	year={1990},
	publisher={JSTOR}
}
@article{dvoretzky1956asymptotic,
	title={Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator},
	author={Dvoretzky, Aryeh and Kiefer, Jack and Wolfowitz, Jacob},
	journal={The Annals of Mathematical Statistics},
	pages={642--669},
	year={1956},
	publisher={JSTOR}
}

@book{vapnik2006estimation,
	title={Estimation of Dependences Based on Empirical Data},
	author={Vapnik, Vladimir},
	year={2006},
	publisher={Springer}
}


@inproceedings{vapnik1968uniform,
	title={The uniform convergence of frequencies of the appearance of events to their probabilities},
	author={Vapnik, Vladimir N and Chervonenkis, Aleksei Yakovlevich},
	booktitle={Doklady Akademii Nauk},
	volume={181},
	number={4},
	pages={781--783},
	year={1968},
	organization={Russian Academy of Sciences}
}

@article{vapnik1971uniform,
	title={Theory of uniform convergence of frequencies of events to their probabilities and problems of search for an optimal solution from empirical data(Average risk minimization based on empirical data, showing relationship of problem to uniform convergence of averages toward expectation value)},
	author={Vapnik, Vladimir N and Chervonenkis, Aleksei Yakovlevich},
	journal={Automation and Remote Control},
	volume={32},
	pages={207--217},
	year={1971}
}

@article{bahadur1956nonexistence,
	title={The nonexistence of certain statistical procedures in nonparametric problems},
	author={Bahadur, Raghu R and Savage, Leonard J},
	journal={The Annals of Mathematical Statistics},
	volume={27},
	number={4},
	pages={1115--1122},
	year={1956},
	publisher={JSTOR}
}
@Article{Lindeberg1922,
	author="Lindeberg, J. W.",
	title="Eine neue {H}erleitung des {E}xponentialgesetzes in der {W}ahrscheinlichkeitsrechnung",
	journal="Mathematische Zeitschrift",
	year="1922",
	month="Dec",
	day="01",
	volume="15",
	number="1",
	pages="211--225",
	issn="1432-1823",
	doi="10.1007/BF01494395",
	url="https://doi.org/10.1007/BF01494395"
}


@book{durrett2010probability,
	title={Probability: {T}heory and examples},
	author={Durrett, Rick},
	year={2010},
	publisher={Cambridge university press}
}

@article{solovay1970model,
	title={A model of set-theory in which every set of reals is {L}ebesgue measurable},
	author={Solovay, Robert M},
	journal={Annals of Mathematics},
	pages={1--56},
	year={1970},
	publisher={JSTOR}
}

@book{elstrodt1996mass,
  title={Ma{\ss}-und Integrationstheorie},
  author={Elstrodt, J{\"u}rgen},
  year={1996},
  publisher={Springer}
}

@misc{hilbert1900mathematische,
	title={Mathematische {P}robleme: {V}ortrag, gehalten auf dem internationalen {M}athematiker-{K}ongre{\ss} zu {P}aris 1900. {N}achrichten der {K}{\"o}niglichen {G}esellschaft der {W}issenschaften zu {G}{\"o}ttingen, mathematisch-physikalische {K}lasse (pp. 253--297)},
	author={Hilbert, David},
	year={1900},
	publisher={G{\"o}ttingen: {V}andenhoeck \& {R}uprecht}
}

@book{georgii2015stochastik,
	title={Stochastik: Einf{\"u}hrung in die Wahrscheinlichkeitstheorie und Statistik},
	author={Georgii, Hans-Otto},
	year={2015},
	publisher={Walter de Gruyter GmbH \& Co KG}
}

@book{kolmogorov1933grundbegriffe,
	title={Grundbegriffe der Wahrscheinlichkeitsrechnung, Berlin, 1933},
	author={Kolmogorov, Andrei Nikolaevich},
	publisher={Springer, Berlin},
	year={1933}
}


@book{hilbertgrundlagen,
	title={Grundlagen der {G}eometrie},
	author={Hilbert, David},
	year={1899},
	publisher={Teubner}
}

@article{mycielski2006system,
	title={A system of axioms of set theory for the rationalists},
	author={Mycielski, Jan},
	journal={Notices of the AMS},
	volume={53},
	number={2},
	pages={206--217},
	year={2006}
}


@book{carath1956,
	title={Gesammelte Mathematische Schriften.},
	author={Carath\'{e}odory, C.},
	publisher={C.H. Beck},
	note={Bd. IV},
	year={1956}
}

@article{Choquet54,
	author = {Choquet, Gustave},
	title = {Theory of capacities},
	journal = {Annales de l'Institut Fourier},
	publisher = {Imprimerie Durand},
	address = {28 - Luisant},
	volume = {5},
	year = {1954},
	pages = {131-295},
	doi = {10.5802/aif.53},
	zbl = {0064.35101},
	mrnumber = {18,295g},
	language = {en},
	url = {http://www.numdam.org/item/AIF_1954__5__131_0}
}

@Article{Dudley1991,
	author="Dudley, R. M.
	and Gin{\'e}, E.
	and Zinn, J.",
	title="Uniform and universal {G}livenko-{C}antelli classes",
	journal="Journal of Theoretical Probability",
	year="1991",
	month="Jul",
	day="01",
	volume="4",
	number="3",
	pages="485--510",
	abstract="A class{\$}{\$}{\backslash}widetilde{\{}F{\}}{\$}{\$}of measurable functions on a probability space is called a Glivenko-Cantelli class if the empirical measuresPnconverge to the trueP uniformly over{\$}{\$}{\backslash}widetilde{\{}F{\}}{\$}{\$}almost surely.{\$}{\$}{\backslash}widetilde{\{}F{\}}{\$}{\$}is a universal Glivenko-Cantelli class if it is a Glivenko-Cantelli Cantelli class for all lawsP on a measurable space, and a uniform Glivenko-Cantelli class if the convergence is also uniform inP. We give general sufficient conditions for the Glivenko-Cantelli and universal Glivenko-Cantelli properties and examples to show that some stronger conditions are not necessary. The uniform Glivenko-Cantelli property is characterized, under measurability assumptions, by an entropy condition.",
	issn="1572-9230",
	doi="10.1007/BF01210321",
	url="https://doi.org/10.1007/BF01210321"
}




@book{denneberg2013,
	title={Non-additive measure and integral},
	author={Denneberg, Dieter},
	volume={27},
	year={2013},
	publisher={Springer Science \& Business Media}
}

@book{walley1991,
	author = {Peter Walley},
	title = {Statistical Reasoning with Imprecise Probabilities},
	publisher = {Chapman \& Hall},
	year = {1991}
}

@book{schmidt2009,
	title={Ma{\ss} und Wahrscheinlichkeit},
	author={Schmidt, Klaus D},
	year={2009},
	publisher={Springer-Verlag}
}


@book{lebesgue1974message,
	title={Message d'un math{\'e}maticien: Henri Lebesgue, pour le centenaire de sa naissance},
	author={Lebesgue, Henri L{\'e}on},
	year={1974},
	publisher={A. Blanchard}
}

@article{lebesgue1972oeuvres,
	title={Oeuvres scientifiques},
	author={Lebesgue, Henri},
	year={1972},
	publisher={Gen{\`e}ve Univ.}
}

@book{forster2016analysis,
  title={Analysis 1: Differential- und Integralrechnung einer Ver{\"a}nderlichen},
  author={Forster, O.},
  series={Grundkurs Mathematik},
  year={2016},
  publisher={Springer Fachmedien Wiesbaden}
}

@book{werner2007funktionalanalysis,
  title={Funktionalanalysis},
  author={Werner, D.},
  isbn={9783540725367},
  series={Springer-Lehrbuch},
  year={2007},
  publisher={Springer Berlin Heidelberg}
}

@book{klenke2006wahrscheinlichkeitstheorie,
  title={Wahrscheinlichkeitstheorie},
  author={Klenke, A.},
  series={Masterclass},
  year={2012},
  publisher={Springer Berlin Heidelberg}
}

@book{Bauer+2011,
title = {Probability Theory},
author = {Heinz Bauer},
year = {2011},
publisher = {De Gruyter}
}

@book{kreyszig1978introductory,
  title={Introductory functional analysis with applications},
  author={Kreyszig, Erwin},
  volume={1},
  year={1978},
  publisher={wiley New York}
}

@book{axler1997linear,
  title={Linear algebra done right},
  author={Axler, Sheldon},
  year={1997},
  publisher={Springer Science \& Business Media}
}

@book{brezis2010functional,
  title={Functional analysis, Sobolev spaces and partial differential equations},
  author={Brezis, Haim},
  year={2010},
  publisher={Springer Science \& Business Media}
}

@article{abellan_additivity_2005,
	title = {Additivity of uncertainty measures on credal sets},
	volume = {34},
	number = {6},
	journal = {International Journal of General Systems},
	author = {Abellán, Joaquín and Klir, George J.},
	year = {2005},
	note = {Publisher: Taylor \& Francis},
	pages = {691--713}
}


@article{abellan_requirements_2008,
	title = {Requirements for total uncertainty measures in {Dempster}–{Shafer} theory of evidence},
	volume = {37},
	number = {6},
	journal = {International journal of general systems},
	author = {Abellán, Joaquin and Masegosa, Andrés},
	year = {2008},
	note = {Publisher: Taylor \& Francis},
	pages = {733--747}
}

@article{abellan_disaggregated_2006,
	title = {Disaggregated total uncertainty measure for credal sets},
	volume = {35},
	number = {1},
	journal = {International Journal of General Systems},
	author = {Abellán, Joaquín and Klir, George J. and Moral, Serafín},
	year = {2006},
	note = {Publisher: Taylor \& Francis},
	pages = {29--44}
}

@article{bengs2022difficulty,
  title={On the Difficulty of Epistemic Uncertainty Quantification in Machine Learning: The Case of Direct Uncertainty Estimation through Loss Minimisation},
  author={Bengs, Viktor and H{\"u}llermeier, Eyke and Waegeman, Willem},
  journal={arXiv preprint arXiv:2203.06102},
  year={2022}
}

@article{radev2021amortized,
  title={Amortized bayesian model comparison with evidential deep learning},
  author={Radev, Stefan T and D'Alessandro, Marco and Mertens, Ulf K and Voss, Andreas and K{\"o}the, Ullrich and B{\"u}rkner, Paul-Christian},
  journal={IEEE Transactions on Neural Networks and Learning Systems},
  year={2021},
  publisher={IEEE}
}

@article{cella2022validity,
  title={Validity, consonant plausibility measures, and conformal prediction},
  author={Cella, Leonardo and Martin, Ryan},
  journal={International Journal of Approximate Reasoning},
  volume={141},
  pages={110--130},
  year={2022},
  publisher={Elsevier}
}

@book{weichselberger2013elementare,
  title={Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung I: Intervallwahrscheinlichkeit als umfassendes Konzept},
  author={Weichselberger, Kurt},
  volume={1},
  year={2013},
  publisher={Springer-Verlag}
}

@article{shafer2008tutorial,
  title={A Tutorial on Conformal Prediction.},
  author={Shafer, Glenn and Vovk, Vladimir},
  journal={Journal of Machine Learning Research},
  volume={9},
  number={3},
  year={2008}
}

@book{vovk2005algorithmic,
  title={Algorithmic learning in a random world},
  author={Vovk, Vladimir and Gammerman, Alexander and Shafer, Glenn},
  year={2005},
  publisher={Springer Science \& Business Media}
}

@book{balasubramanian2014conformal,
  title={Conformal prediction for reliable machine learning: theory, adaptations and applications},
  author={Balasubramanian, Vineeth and Ho, Shen-Shyang and Vovk, Vladimir},
  year={2014},
  publisher={Newnes}
}

@article{hullermeier2014learning,
  title={Learning from imprecise and fuzzy observations: Data disambiguation through generalized loss minimization},
  author={H{\"u}llermeier, Eyke},
  journal={International Journal of Approximate Reasoning},
  volume={55},
  number={7},
  pages={1519--1534},
  year={2014},
  publisher={Elsevier}
}

@article{hullermeier2006learning,
  title={Learning from ambiguously labeled examples},
  author={H{\"u}llermeier, Eyke and Beringer, J{\"u}rgen},
  journal={Intelligent Data Analysis},
  volume={10},
  number={5},
  pages={419--439},
  year={2006},
  publisher={IOS Press}
}

@article{hora1996aleatory,
  title={Aleatory and epistemic uncertainty in probability elicitation with an example from hazardous waste management},
  author={Hora, Stephen C},
  journal={Reliability Engineering \& System Safety},
  volume={54},
  number={2-3},
  pages={217--223},
  year={1996},
  publisher={Elsevier}
}

@article{hullermeier2021aleatoric,
  title={Aleatoric and epistemic uncertainty in machine learning: An introduction to concepts and methods},
  author={H{\"u}llermeier, Eyke and Waegeman, Willem},
  journal={Machine Learning},
  volume={110},
  number={3},
  pages={457--506},
  year={2021},
  publisher={Springer}
}

@book{augustin2014introduction,
  title={Introduction to imprecise probabilities},
  author={Augustin, Thomas and Coolen, Frank PA and De Cooman, Gert and Troffaes, Matthias CM},
  year={2014},
  publisher={John Wiley \& Sons}
}

@article{ellsberg,
	author = {Daniel Ellsberg},
	journal = {The Quarterly Journal of Economics},
	number = {4},
	pages = {643--669},
	publisher = {Oxford University Press},
	title = {Risk, Ambiguity, and the {S}avage Axioms},
	volume = {75},
	year = {1961}}

@article{eyke2,
	author = {Eyke Hüllermeier},
	journal = {Available at \href{https://arxiv.org/abs/2209.03302}{arxiv:2209.03302}},
	title = {Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?},
	year = {2022}}

@article{cuzzo,
	author = {Shireen Kudukkil Manchingal and Fabio Cuzzolin},
	journal = {Available at arxiv:2206.07609},
	title = {Epistemic Deep Learning},
	year = {2022}}	


@book{cuzzo2,
	author = {Fabio Cuzzolin},
	publisher = {Springer Nature Switzerland},
	series = {Artificial Intelligence: Foundations, Theory, and Algorithms},
	title = {The Geometry of Uncertainty},
        subtitle={The Geometry of Imprecise Probabilities},
	year = {2021}}

@article{teddy_sei,
title = {Forecasting with imprecise probabilities},
journal = {International Journal of Approximate Reasoning},
volume = {53},
number = {8},
pages = {1248--1261},
year = {2012},
note = {Imprecise Probability: Theories and Applications (ISIPTA'11)},
author = {Teddy Seidenfeld and Mark J. Schervish and Joseph B. Kadane}
}

@inbook{anel, 
place={Cambridge}, 
title={The Geometry of Ambiguity: An Introduction to the Ideas of Derived Geometry}, 
volume={1}, 
booktitle={New Spaces in Mathematics: Formal and Conceptual Reflections}, 
publisher={Cambridge University Press}, 
author={Mathieu Anel}, 
year={2021}, 
pages={505--553}
}

@article{bloch,
title = {Some aspects of {D}empster-{S}hafer evidence theory for classification of multi-modality medical images taking partial volume effect into account},
journal = {Pattern Recognition Letters},
volume = {17},
number = {8},
pages = {905--919},
year = {1996},
author = {Isabelle Bloch}
}

@article{hifi,
	author = {Mhand Hifi and Labib Yousef},
	journal = {European Journal of Operational Research},
	pages = {482--500},
	title = {A local search-based method for sphere packing problems},
	volume = {247},
	year = {2019}}

@article{maryna,
	author = {Maryna S. Viazovska},
	journal = {Annals of Mathematics},
	pages = {991--1015},
	title = {The sphere packing problem in dimension 8},
	volume = {185},
        number={3},
	year = {2017}}


@article{cohn,
 author = {Henry Cohn and Abhinav Kumar and Stephen D. Miller and Danylo Radchenko and Maryna S. Viazovska},
 journal = {Annals of Mathematics},
 number = {3},
 pages = {1017--1033},
 publisher = {Annals of Mathematics},
 title = {The sphere packing problem in dimension 24},
 volume = {185},
 year = {2017}
}

@article{senge_2014_ReliableClassificationLearning,
  title = {Reliable Classification: {{Learning}} Classifiers That Distinguish Aleatoric and Epistemic Uncertainty},
  shorttitle = {Reliable Classification},
  author = {Senge, Robin and Bösner, Stefan and Dembczyński, Krzysztof and Haasenritter, Jörg and Hirsch, Oliver and Donner-Banzhoff, Norbert and Hüllermeier, Eyke},
  year = {2014},
  journal = {Information Sciences},
  shortjournal = {Information Sciences},
  volume = {255},
  pages = {16--29},
  optIssn = {00200255},
  optDoi = {10.1016/j.ins.2013.07.030}
}

@article{lambrou2010reliable,
  title={Reliable confidence measures for medical diagnosis with evolutionary algorithms},
  author={Lambrou, Antonis and Papadopoulos, Harris and Gammerman, Alex},
  journal={IEEE Transactions on Information Technology in Biomedicine},
  volume={15},
  number={1},
  pages={93--99},
  year={2010},
  publisher={IEEE}
}

@article{yang2009using,
  title={Using random forest for reliable classification and cost-sensitive learning for medical diagnosis},
  author={Yang, Fan and Wang, Hua-zhen and Mi, Hong and Lin, Cheng-de and Cai, Wei-wen},
  journal={BMC bioinformatics},
  volume={10},
  number={1},
  pages={1--14},
  year={2009},
  publisher={BioMed Central}
}

@inproceedings{varshney2016engineering,
  title={Engineering safety in machine learning},
  author={Varshney, Kush R},
  booktitle={2016 Information Theory and Applications Workshop (ITA)},
  pages={1--5},
  year={2016},
  organization={IEEE}
}

@article{varshney2017safety,
  title={On the safety of machine learning: Cyber-physical systems, decision sciences, and data products},
  author={Varshney, Kush R and Alemzadeh, Homa},
  journal={Big data},
  volume={5},
  number={3},
  pages={246--255},
  year={2017},
  publisher={Mary Ann Liebert, Inc. 140 Huguenot Street, 3rd Floor New Rochelle, NY 10801 USA}
}

@article{kendall2017uncertainties,
  title={What uncertainties do we need in bayesian deep learning for computer vision?},
  author={Kendall, Alex and Gal, Yarin},
  journal={Advances in neural information processing systems},
  volume={30},
  year={2017}
}

@article{smith2018understanding,
  title={Understanding measures of uncertainty for adversarial example detection},
  author={Smith, Lewis and Gal, Yarin},
  journal={arXiv preprint arXiv:1803.08533},
  year={2018}
}

@inproceedings{depeweg2018decomposition,
  title={Decomposition of uncertainty in Bayesian deep learning for efficient and risk-sensitive learning},
  author={Depeweg, Stefan and Hernandez-Lobato, Jose-Miguel and Doshi-Velez, Finale and Udluft, Steffen},
  booktitle={International Conference on Machine Learning},
  pages={1184--1193},
  year={2018},
  organization={PMLR}
}

@article{kapoor2022uncertainty,
  title={On Uncertainty, Tempering, and Data Augmentation in Bayesian Classification},
  author={Kapoor, Sanyam and Maddox, Wesley J and Izmailov, Pavel and Wilson, Andrew Gordon},
  journal={arXiv preprint arXiv:2203.16481},
  year={2022}
}

@book{Knight1921,
  title = {Risk, Uncertainty and Profit},
  author = {{Knight, Frank H.}},
  year = {1921},
  publisher = {Houghton Mifflin Co}
}

@book{villani2009optimal,
  title={Optimal transport: old and new},
  author={Villani, C{\'e}dric},
  volume={338},
  year={2009},
  publisher={Springer}
}

@book{villani2021topics,
  title={Topics in optimal transportation},
  author={Villani, C{\'e}dric},
  volume={58},
  year={2021},
  publisher={American Mathematical Soc.}
}

@article{rubner2000earth,
  title={The earth mover's distance as a metric for image retrieval},
  author={Rubner, Yossi and Tomasi, Carlo and Guibas, Leonidas J},
  journal={International journal of computer vision},
  volume={40},
  number={2},
  pages={99--121},
  year={2000},
  publisher={Springer}
}

@article{ni2009local,
  title={Local histogram based segmentation using the Wasserstein distance},
  author={Ni, Kangyu and Bresson, Xavier and Chan, Tony and Esedoglu, Selim},
  journal={International journal of computer vision},
  volume={84},
  number={1},
  pages={97--111},
  year={2009},
  publisher={Springer}
}

@article{sicking2022wasserstein,
  title={Wasserstein dropout},
  author={Sicking, Joachim and Akila, Maram and Pintz, Maximilian and Wirtz, Tim and Wrobel, Stefan and Fischer, Asja},
  journal={Machine Learning},
  pages={1--44},
  year={2022},
  publisher={Springer}
}

@article{panaretos2019statistical,
  title={Statistical aspects of Wasserstein distances},
  author={Panaretos, Victor M and Zemel, Yoav},
  journal={Annual review of statistics and its application},
  volume={6},
  pages={405--431},
  year={2019},
  publisher={Annual Reviews}
}

@inproceedings{hullermeier2022quantification,
  title={Quantification of credal uncertainty in machine learning: A critical analysis and empirical comparison},
  author={H{\"u}llermeier, Eyke and Destercke, S{\'e}bastien and Shaker, Mohammad Hossein},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={548--557},
  year={2022},
  organization={PMLR}
}

@incollection{corani2012bayesian,
  title={Bayesian networks with imprecise probabilities: Theory and application to classification},
  author={Corani, Giorgio and Antonucci, Alessandro and Zaffalon, Marco},
  booktitle={Data Mining: Foundations and Intelligent Paradigms},
  pages={49--93},
  year={2012},
  publisher={Springer}
}

@article{walley1991statistical,
  title={Statistical reasoning with imprecise probabilities},
  author={Walley, Peter},
  year={1991}
}

@article{abellan2003building,
  title={Building classification trees using the total uncertainty criterion},
  author={Abell{\'a}n, Joaqu{\'\i}n and Moral, Seraf{\'\i}n},
  journal={International Journal of Intelligent Systems},
  volume={18},
  number={12},
  pages={1215--1225},
  year={2003},
  publisher={Wiley Online Library}
}

@inproceedings{bronevich2008axioms,
  title={Axioms for uncertainty measures on belief functions and credal sets},
  author={Bronevich, Andrey and Klir, George J},
  booktitle={NAFIPS 2008-2008 Annual Meeting of the North American Fuzzy Information Processing Society},
  pages={1--6},
  year={2008},
  organization={IEEE}
}

@article{bronevich2010measures,
  title={Measures of uncertainty for imprecise probabilities: an axiomatic approach},
  author={Bronevich, Andrey and Klir, George J},
  journal={International journal of approximate reasoning},
  volume={51},
  number={4},
  pages={365--390},
  year={2010},
  publisher={Elsevier}
}



@article{caprio_IBNN,
  title={{Imprecise Bayesian Neural Networks}},
  author={Michele Caprio and Souradeep Dutta and Radoslav Ivanov and Kuk Jang and Vivian Lin and Oleg Sokolsky and Insup Lee},
  journal={arXiv preprint arXiv:2302.09656},
  year={2023}
}






@techreport{caprio_INN,
     title = {{EpiC INN: Epistemic Curiosity Imprecise Neural Network}},
     author = {Michele Caprio and Souradeep Dutta and Kaustubh Sridhar and Kuk Jang and Vivian Lin and Oleg Sokolsky and Insup Lee},
     group = {PRECISE},
     year = {2023},
     institution = {University of Pennsylvania, Department of Computer and Information Science},
     month = {01}
}

@inproceedings{shaker2020aleatoric,
  title={Aleatoric and epistemic uncertainty with random forests},
  author={Shaker, Mohammad Hossein and H{\"u}llermeier, Eyke},
  booktitle={Advances in Intelligent Data Analysis XVIII: 18th International Symposium on Intelligent Data Analysis, IDA 2020, Konstanz, Germany, April 27--29, 2020, Proceedings 18},
  pages={444--456},
  year={2020},
  organization={Springer}
}

@inproceedings{bengs2022pitfalls,
  title={Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation},
  author={Bengs, Viktor and H{\"u}llermeier, Eyke and Waegeman, Willem},
  booktitle={Advances in Neural Information Processing Systems},
  year={2022}
}

@article{shannon1948mathematical,
  title={A mathematical theory of communication},
  author={Shannon, Claude E},
  journal={The Bell system technical journal},
  volume={27},
  number={3},
  pages={379--423},
  year={1948},
  publisher={Nokia Bell Labs}
}

@article{pal1992uncertainty,
  title={Uncertainty measures for evidential reasoning I: A review},
  author={Pal, Nikhil R and Bezdek, James C and Hemasinha, Rohan},
  journal={International Journal of Approximate Reasoning},
  volume={7},
  number={3-4},
  pages={165--183},
  year={1992},
  publisher={Elsevier}
}

@article{pal1993uncertainty,
  title={Uncertainty measures for evidential reasoning II: A new measure of total uncertainty},
  author={Pal, Nikhil R and Bezdek, James C and Hemasinha, Rohan},
  journal={International Journal of Approximate Reasoning},
  volume={8},
  number={1},
  pages={1--16},
  year={1993},
  publisher={Elsevier}
}

@article{abellan2003maximum,
  title={Maximum of entropy for credal sets},
  author={Abellan, Joaquin and Moral, Serafin},
  journal={International journal of uncertainty, fuzziness and knowledge-based systems},
  volume={11},
  number={05},
  pages={587--597},
  year={2003},
  publisher={World Scientific}
}

@article{abellan2000non,
  title={A non-specificity measure for convex sets of probability distributions},
  author={Abell{\'a}n, Joaqu{\'\i}n and Moral, Seraf{\'\i}n},
  journal={International journal of uncertainty, fuzziness and knowledge-based systems},
  volume={8},
  number={03},
  pages={357--367},
  year={2000},
  publisher={World Scientific}
}

@book{vershynin2018high,
  title={High-dimensional probability: An introduction with applications in data science},
  author={Vershynin, Roman},
  volume={47},
  year={2018},
  publisher={Cambridge university press}
}

@article{zaffalon2002naive,
  title={The naive credal classifier},
  author={Zaffalon, Marco},
  journal={Journal of statistical planning and inference},
  volume={105},
  number={1},
  pages={5--21},
  year={2002},
  publisher={Elsevier}
}

@article{corani2008learning,
  title={Learning Reliable Classifiers From Small or Incomplete Data Sets: The Naive Credal Classifier 2.},
  author={Corani, Giorgio and Zaffalon, Marco},
  journal={Journal of Machine Learning Research},
  volume={9},
  number={4},
  year={2008}
}

@article{walley1996inferences,
  title={Inferences from multinomial data: learning about a bag of marbles},
  author={Walley, Peter},
  journal={Journal of the Royal Statistical Society: Series B (Methodological)},
  volume={58},
  number={1},
  pages={3--34},
  year={1996},
  publisher={Wiley Online Library}
}



@techreport{settles2009active,
     title = {{Active Learning Literature Survey}},
     author = {Settles, Burr},
     year = {2009},
     institution = {University of Wisconsin-Madison, Department of Computer Sciences}
}