MILAN STUDENÝ - HOME PAGE

Affiliation

Milan Studený

Academy of Sciences of the Czech Republic

Institute of Information Theory and Automation

Pod Vodárenskou věží 4

18200 Prague 8 Libeň

Czech Republic

Home mail address

Bryksova 951/13

19800 Prague 14 Černý Most II

Czech Republic

Other connections

Phone (job): (420-) 2 6605 2304

Fax: (420-) 2 688 4903 (institute)

E-mail: studeny@utia.cas.cz

Home phone: (420-) 2 81911 553

Research interests

formal properties of conditional independence (also in different calculi of AI)
using graphs for modeling conditional independence structure (Bayesian networks, chain graphs)
probabilistic knowledge based systems
marginal problem
learning Bayesian networks
game theory
information theory

Some web references

seminar Algorithmic Aspects of Information Theory to be organized by Leibniz Center for Informatics, July 24-29, 2022, Schloss Dagstuhl, Germany.
Workshop in memory of Frantisek Matus within PRAGUE STOCHASTICS 2019, August 19-23, 2019, Prague, Czech Republic.
the 9th International Conference on Probabilistic Graphical Models (PGM 2018) September 11-14, 2018, Prague, Czech Republic.
workshop on Algebraic Statistics within PRAGUE STOCHASTICS 2014, August 25-29, 2014, Prague, Czech Republic.
the 3rd European Workshop on Probabilistic Graphical Models (PGM'06) September 12-15, 2006, Prague, Czech Republic.

List of publications

pdf version of the list of publications (March 2023)

Selected publications (updated on May 29, 2023)

Some recent publications:

M. Studeny: Conditional independence structures over four discrete random variables revisited: conditional Ingleton inequalities. IEEE Transactions on Information Theory 67 (2021), n. 11, pp. 7030-7049. For an abstract click here. A pdf version of a preprint (343kB) is available.
M. Studeny: Contribution of Frantisek Matus to the research on conditional independence. Kybernetika 56 (2020), pp. 850-874.
For an abstract click here. A pdf version of the published paper (413kB) is available.

M. Studeny, V. Kratochvil: Facets of the cone of exact games. Mathematical Methods of Operations Research 95 (2022), n. 1, pp. 35-800. For an abstract click here. A pdf version of a preprint (448kB) is available. Moreover, the result of the work is also an interactive electronic catalogue of indecomposable min-semi-balanced system on at most 6 variables.
T. Kroupa, M. Studeny: Facets of the cone of totally balanced games. Mathematical Methods of Operations Research 90 (2019), pp. 271-300. For an abstract click here. A pdf version of a preprint (338kB) is available.
M. Studeny, V. Kratochvil: Linear criterion for testing the extremity of an exact game based on its finest min-representation. International Journal of Approximate Reasoning 101 (2018), pp. 49-68. For an abstract click here. A pdf version of a preprint (262kB) is available. The result of the work is also an interactive implementation of the criterion to recognize extremity of an exact game.

M. Studeny, J. Cussens, V. Kratochvil: The dual polyhedron to the chordal graph polytope and the rebuttal of the chordal graph conjecture. International Journal of Approximate Reasoning 138 (2021), pp. 188-203. For an abstract click here. A pdf version of a preprint (266kB) is available.

Axiomatic properties of conditional independence

M. Studeny: Multiinformation and the problem of characterization of conditional independence relations. Problems of Control and Information Theory 18 (1989), n. 1, pp. 3-16.
For an abstract click here. A scanned pdf copy (5655kB) is available.
M. Studeny: Attempts at axiomatic description of conditional independence. Kybernetika 25 (1989), supplement to n. 3, pp. 72-79.
For an abstract click here. A scanned pdf copy (717kB) is available.
M. Studeny: Conditional independence relations have no finite complete characterization. In Information Theory, Statistical Decision Functions and Random Processes. Transactions of the 11th Prague Conference vol. B (S. Kubik, J.A. Visek eds.) Kluwer, Dordrecht - Boston - London (also Academia, Prague) 1992, pp. 377-396.
For an abstract click here. A pdf copy (converted postscript version) (253kB) is available.
M. Studeny: Semigraphoids are two-antecedental approximations of stochastic conditional independence models. In Uncertainty in Artificial Intelligence. Proceedings of the Tenth Conference (R.L. de Mantaras, D. Poole eds.), Morgan Kaufmann, San Francisco CA 1994, pp. 546-552.
For an abstract click here. A scanned pdf copy (1119kB) is available.
M. Studeny: Semigraphoids and structures of probabilistic conditional independence. Annals of Mathematics and Artificial Intelligence 21 (1997), n. 1, pp. 71-98.
For an abstract click here. A pdf version (440kB) is available.
M. Studeny: Contribution of Frantisek Matus to the research on conditional independence. Kybernetika 56 (2020), pp. 850-874.
For an abstract click here. A pdf version of the published paper (413kB) is available.

Description of conditional independence structures

M. Studeny: Structural semigraphoids. International Journal of General Systems 22 (1994), n. 2, pp. 207-217. For an abstract click here. A scanned pdf copy (698kB) is available.
M. Studeny: Description of structures of stochastic conditional independence by means of faces and imsets. 1st part: introduction and basic concepts. International Journal of General Systems 23 (1994), n. 2, pp. 123-137. For an abstract click here. A scanned pdf copy (925kB) is available.
M. Studeny: Description of structures of stochastic conditional independence by means of faces and imsets. 2nd part: basic theory. International Journal of General Systems 23 (1995), n. 3, pp. 201-219.
For an abstract click here. A scanned pdf copy (1050kB) is available.
M. Studeny: Description of structures of stochastic conditional independence by means of faces and imsets. 3rd part: examples of use and appendices. International Journal of General Systems 23 (1995), n. 4, pp. 323-341. For an abstract click here. A scanned pdf copy (1048kB) is available.
M. Studeny: Description of conditional independence structures by means of imsets: a connection with product formula validity. In Uncertainty in Intelligent Systems (B. Bouchon-Meunier, L. Valverde, R.R. Yager eds.) North-Holland, Amsterdam - London - New York - Tokyo 1993, pp. 179-194.
For an abstract click here. A pdf copy (converted postscript version) (229kB) is available.
M. Studeny: Complexity of structural models. In Prague Stochastics'98. Proceedings of the Joint Session of the 6th Prague Conference on Asymptotic Statistics and the 13th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes vol. II, August 23-28, 1998, Prague, Czech Republic, pp. 521-528.
For an abstract click here. A pdf copy (converted postscript version) (185kB) is available.
M. Studeny: On non-graphical description of models of conditional independence structure. Paper presented at HSSS Workshop on Stochastic Systems for Individual Behaviours, January 22-23, 2001, Louvain la Neuve, Belgium (15 pages).
For an abstract click here. A pdf version (235kB) is available.
M. Studeny: On mathematical description of probabilistic conditional independence structures, thesis for DrSc degree, Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague, May 2001, 192 pages.
For an abstract click here. A pdf copy (converted postscript version) (1439kB) is available. WARNING: the file is very long, it has 192 pages and contains some colorful pictures.
Note it the thesis was the basis for later book M. Studeny: Probabilistic Conditional Independence Structures, Springer London 2005 (series Information Science and Statistics).
Contact Springer-Verlag if you wish to buy the book.
M. Studeny: On stochastic conditional independence: the problems of characterization and description. Annals of Mathematics and Artificial Intelligence 35 (2002), pp. 323-241.
For an abstract click here. A pdf copy of a preprint (209kB) is available.
P. Simecek, M. Studeny: Vyuziti pojmu Hilbertovy baze pro overovani hypotezy o shodnosti strukturalnich a kombinatorickych imsetu (in Czech, translation: The use of the concept of a Hilbert basis to verify a hypothesis about the coincidence of structural and combinatorial imsets), in ROBUST 2004 Sbornik praci trinacte letni skoly JCMF (J. Antoch, G. Dohnal eds.), Trest, Czech Republic, JCMF 2004, pp. 395-401.
For an abstract click here. A pdf version (178kB) is available.
M. Studeny: Structural imsets: an algebraic method for describing conditional independence structures. In Proceedings of the 10th International Conference IPMU 2004 (B. Bouchon-Meunier, G. Colleti, R. R. Yager eds.), Editrice Universita La Sapienza, Perugia, Italy, 2004, vol. 2, pp. 1323-1330.
For an abstract click here. A pdf copy of a preprint (285kB) is available.
M. Studeny: Conditional independence and Markov properties for basic graphs. In Handbook of Graphical Models (M. Maathuis, M. Drton, S. Lauritzen, M. Wainwright eds.) Chapman and Hall/CRC, 2018, pages 3-38.
For an abstract click here. A pdf version of (230kB) is available.

Conditional independence inference

M. Studeny: Structural imsets: an algebraic method for describing conditional independence structures. In Proceedings of the 10th International Conference IPMU 2004 (B. Bouchon-Meunier, G. Colleti, R. R. Yager eds.), Editrice Universita La Sapienza, Perugia, Italy, 2004, vol. 2, pp. 1323-1330.
For an abstract click here. A pdf copy of a preprint (285kB) is available.
R. R. Bouckaert, M. Studeny: Racing algorithms for conditional independence inference. International Journal of Approximate Reasoning 45 (2007), pp. 386-401.
For an abstract click here. A scanned pdf copy of the published paper (1112kB) is already open-access available.
R. Bouckaert, R. Hemmecke, S. Lindner, M. Studeny: Efficient algorithms for conditional independence inference. Journal of Machine Learning Research 11 (2010), pp. 3453-3479.
For an abstract click here. A pdf version of the paper (218kB) is available.
K. Tanaka, M. Studeny, A. Takemura, T. Sei: A linear-algebraic tool for conditional independence inference. Journal of Algebraic Statistics 6 (2015), n. 2, pp. 150-167.
For an abstract click here. A pdf version of the published paper (424kB) is available.

Conditional independence structures over four variables

M. Studeny and P. Bocek: CI-models arising among 4 random variables. In Proceedings of the 3rd workshop WUPES, September 11-15, 1994, Trest, Czech Republic, pp. 268-282. For an abstract click here. A pdf copy (converted postscript version) (192kB) is available.
F. Matus and M. Studeny: Conditional independences among four random variables I. Combinatorics, Probability and Computing 4 (1995), n. 3, pp. 267-278. For an abstract click here. This is the first paper of a series of papers written by Frantisek Matus. A pdf copy (converted postscript version) (194kB) is available.
M. Studeny: Conditional independence structures over four discrete random variables revisited: conditional Ingleton inequalities. IEEE Transactions on Information Theory 67 (2021), n. 11, pp. 7030-7049. For an abstract click here. A pdf version of a preprint (343kB) is available.

Extreme supermodular functions/games (in context of conditional independence)

M. Studeny, R.R. Bouckaert, T. Kocka: Extreme supermodular set functions over five variables. Research report n. 1977, Institute of Information Theory and Automation, Prague, January 2000 (32 pages). For an abstract click here. A pdf copy (269kB) is available.
Moreover, the result of the work is also an electronic catalogue of representatives extreme supermodular set functions over five variables.
M. Studeny, T. Kroupa: Core-based criterion for extreme supermodular functions. Discrete Applied Mathematics 206 (2016), pp. 122-151. For an abstract click here. A pdf version of the published paper (635kB) is available.
The presented criterion has recently been implemented and an interactive web platform is available which allows the user to recognize the extremity of a supermodular game over at most 8 players.
M. Studeny: Basic facts concerning extreme supermodular functions. Research report n. 2359, Institute of Information Theory and Automation, Prague, December 2016. For an abstract click here. A pdf version (434kB) is available. See also its arxiv version 1612.06599

Game theory

M. Studeny, V. Kratochvil: Linear core-based criterion for testing extreme exact games. In JMLR Workshops and Conference Proceedings 62 (2017), Proceedings of ISIPTA 2017, pp. 313-324.
For an abstract click here. A pdf version (237kB) is available.
M. Studeny, V. Kratochvil: Linear criterion for testing the extremity of an exact game based on its finest min-representation. International Journal of Approximate Reasoning 101 (2018), pp. 49-68. For an abstract click here. A pdf version of a preprint (262kB) is available.
The result of the work is also an interactive implementation of the criterion to recognize extremity of an exact game.
T. Kroupa, M. Studeny: Facets of the cone of totally balanced games. Mathematical Methods of Operations Research 90 (2019), pp. 271-300. For an abstract click here. A pdf version of a preprint (338kB) is available.
M. Studeny, V. Kratochvil, J. Vomlel: On irreducible min-balanced set systems. In Symbolic and Quantitative Approaches to Reasoning with Uncertainty (G. Kern-Isberner, Z. Ognjanovic eds.), Lecture Notes in Artificial Intelligence 1126, Springer-Verlag, Cham 2019, pp. 444-454.
For an abstract click here. A pdf version of a preprint (299kB) is available.
Moreover, the result of the work is also an interactive electronic catalogue of min-balanced system on at most 5 variables.
M. Studeny, V. Kratochvil: Facets of the cone of exact games. Mathematical Methods of Operations Research 95 (2022), n. 1, pp. 35-800. For an abstract click here. A pdf version of a preprint (448kB) is available. Moreover, the result of the work is also an interactive electronic catalogue of indecomposable min-semi-balanced system on at most 6 variables.

Measures of dependence

M. Studeny: Pojem multiinformace v pravdepodobnostnim rozhodovani. (in Czech, translation: The notion of multiinformation in probabilistic decision making), doctoral thesis, Czechoslovak Academy of Sciences, Institute of Information Theory and Automation, Prague 1987, Czechoslovakia, 121 pages.
A pdf abstract (147kB) is available.
M. Studeny: Asymptotic behaviour of empirical multiinformation. Kybernetika 23 (1987), n. 2, pp. 124-135. For an abstract click here. A scanned pdf copy (526kB) is available.
J. Zvarova and M. Studeny: Information theoretical approach to constitution and reduction of medical data. International Journal of Medical Informatics 45 (1997), n. 1-2, pp. 65-74.
For an abstract click here. A scanned pdf copy (917kB) is available.
M. Studeny and J. Vejnarova: The multiinformation function as a tool for measuring stochastic dependence. In Learning in Graphical Models (M. I. Jordan ed.) Kluwer, Dordrecht 1998, pp. 261-298.
For an abstract click here. A pdf copy (converted postscript version) (366kB) is available.

Conditional independence in non-probabilistic calculi

M. Studeny: Formal properties of conditional independence in different calculi of AI. In Symbolic and Quantitative Approaches to Reasoning and Uncertainty (M. Clarke, R. Kruse, S. Moral eds.), Springer-Verlag, Berlin -Heidelberg 1993, pp. 341-348.
For an abstract click here. A pdf copy (converted postscript version) (272kB) is available.
M. Studeny: Conditional independence and natural conditional functions. International Journal of Approximate Reasoning 12 (1995), n. 1, pp. 43-68.
For an abstract click here. A scanned pdf copy (1141kB) is available.
A. P. Dawid, M. Studeny: Conditional products: an alternative approach to conditional cndependence. In Artificial Intelligence and Statistics 99. Proceedings of the 7th Workshop (D. Heckerman, J. Whittaker eds.), Morgan Kaufmann, San Francisco 1999, pp. 32-40.
For an abstract click here. A pdf copy (converted postscript version) (205kB) is available.

Chain graphs

R. R. Bouckaert and M. Studeny: Chain graphs: semantics and expressiveness. In Symbolic and Quantitative Approaches to Reasoning and Uncertainty (Ch. Froidevaux, J. Kohlas eds.), Lecture Notes in Artificial Intelligence 946 (subseries of Lecture Notes in Computer Science), Springer-Verlag, Berlin - Heidelberg 1995, pp. 69-76.
For an abstract click here. A pdf copy (converted postscript version) (174kB) is available.
M. Studeny: On separation criterion and recovery algorithm for chain graphs. In Uncertainty in Artificial Intelligence. Proceedings of the 12th Conference (E. Horvitz, F. Jensen eds.), Morgan Kaufmann, San Francisco 1996, pp. 509-516.
For an abstract click here. A pdf copy (converted postscript version) (1167kB) is available.
M. Studeny: A recovery algorithm for chain graphs. International Journal of Approximate Reasoning 17 (1997), n. 2-3, pp. 265-293.
For an abstract click here. A scanned pdf copy (1482kB) is available.
M. Studeny and R. R. Bouckaert: On chain graph models for description of conditional independence structures. The Annals of Statistics 26 (1998), n. 4, pp. 1434-1495.
For an abstract click here. A pdf copy of the published paper (374kB) is already open-access available.
M. Studeny: Bayesian networks from the point of view of chain graphs. In Uncertainty in Artificial Intelligence. Proceedings of the 14th Conference (G. F. Cooper, S. Moral eds.), Morgan Kaufmann, San Francisco 1998, pp. 496-503.
For an abstract click here. A pdf copy (343kB) is available.
M. Volf and M. Studeny: A graphical characterization of the largest chain graphs. International Journal of Approximate Reasoning 20 (1999), pp. 209-236.
For an abstract click here. A scanned pdf copy of the paper (1188kB) is already open-access available.
M. Studeny: O pouziti retezcovych grafu pro popis struktur podminene nezavislosti (in Czech, translation: On the use of chain graphs for the description of conditional independence structures) In ROBUST'2002. Sbornik praci dvacate zimni skoly JCMF, Hejnice, Ceska republika, pp. 292-314.
This is an overview paper in Czech written for students of statistics. The topic of the paper are basic graphical tools for the description of conditional independence structures.
For an abstract (in Czech) click here. A pdf copy (converted postscript version) (330kB) is available.
M. Studeny: Characterization of essential graphs by means of the operation of legal merging of components. International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems 12 (2004), supplement 1, pp. 43-62. For an abstract click here. A pdf copy of the paper (1190kB) only for academic/personal use is available.
A. Roverato, M. Studeny: A graphical representation of equivalence classes of AMP chain graphs. Journal of Machine Learning Research 7 (2006), pp. 1045-1078.
For an abstract click here. A pdf version of the paper (308kB) is available.
M. Studeny, A. Roverato, S. Stepanova: Two operations of merging and splitting components in a chain graph. Kybernetika 45 (2009), n. 2, pp. 208-248.
For an abstract click here. A pdf version of the published paper (451kB) is available.

Learning Bayesian networks

T. Kocka, R. R. Bouckaert, M. Studeny: On characterizing inclusion of Bayesian networks. In Uncertainty in Artificial Intelligence. Proceedings of the 17th Conference (J. Breese, D. Koller eds.), Morgan Kaufmann, San Francisco 2001, pp. 261-268.
For an abstract click here. A scanned pdf copy (1012kB) is available.
T. Kocka, R. R. Bouckaert, M. Studeny: On the inclusion problem. Research report n. 2010, Institute of Information Theory and Automation, Prague, February 2001.
For an abstract click here. A pdf copy (310kB) is available.
M. Studeny: An algebraic approach to learning Bayesian networks. In the book of abstracts of the 7th International Valencia Meeting on Bayesian Statistics, Playa de las Americas, Tenerife, Spain, June 1-6, 2002, p.179. For an abstract click here. A pdf version (converted postscript version) of posters (294kB) is available.
M. Studeny: Characterization of inclusion neighbourhood in terms of the essential graphs. International Journal of Approximate Reasoning 38 (2005), n. 3, pp. 283-309.
For an abstract click here. A scanned pdf copy (478kB) is available.
M. Studeny: An algebraic approach to structural learning Bayesian networks. In Proceedings of the 11th International Conference IPMU 2006 (B. Bouchon-Meunier, R. R. Yager eds.), Editions EDK, Paris, France 2006, pp. 2284-2291.
For an abstract click here. A pdf version (227kB) is available.
J. Vomlel, M. Studeny: Graphical and algebraic representatives of conditional independence models. In Advances in Bayesian Networks (P. Lucas, J. A. Gamez, A. Salmeron eds.), Studies in Fuzziness and Soft Computing 213, Springer 2007, pages 55-80.
For an abstract click here. A pdf version of a preprint (268kB) is available.
M. Studeny, J. Vomlel: A reconstruction algorithm for the essential graph. International Journal of Approximate Reasoning 50 (2009), n. 2, pp. 385-413.
For an abstract click here. A pdf version of the published paper (708kB) is already open-access available.
M. Studeny: Mathematical aspects of learning Bayesian networks: Bayesian quality criteria. Research report n. 2234, Institute of Information Theory and Automation, Prague, December 2008.
For an abstract click here. A pdf version (484kB) is available.

Geometric approach to learning (Bayesian networks)

M. Studeny, R. Hemmecke, S. Lindner: Characteristic imset: a simple algebraic representative of a Bayesian network structure. In Proceedings of the 5th European Workshop on Probabilistic Graphical Models (P. Myllymaki, T. Roos and T. Jaakkola eds.), HIIT Publications 2010-2, pp. 257-264. For an abstract click here. A pdf version (154kB) is available.
M. Studeny, J. Vomlel, R. Hemmecke: Geometric view on learning Bayesian network structures. International Journal of Approximate Reasoning 51 (2010), n. 5, pp. 578-586.
For an abstract click here. A pdf version of the published paper (402kB) is already open-access available. A related document is also an earlier web page Geometric neighborhood for Bayesian network structures .. prepared by J. Vomlel.
M. Studeny, J. Vomlel: On open questions in the geometric approach to structural learning Bayesian nets. International Journal of Approximate Reasoning 52 (2011), n. 5, pp. 627-640.
For an abstract click here. A pdf version of the published paper (262kB) is already open-access available. An extension of that paper is a web page The catalogue of types of geometric neighbors over four variables prepared by J. Vomlel.
R. Hemmecke, S. Lindner, M. Studeny: Characteristic imsets for learning Bayesian network structure. International Journal of Approximate Reasoning 53 (2012), n. 9, pp. 1336-1349.
For an abstract click here. A pdf version of the published paper (337kB) is already open-access available.
M. Studeny, D. Haws, R. Hemmecke, S. Lindner: Polyhedral approach to statistical learning graphical models. In Harmony of Groebner Bases and the Modern Industrial Society: the 2nd CREST--SBM International Conference (T. Hibi ed.), World Scientific, Singapore 2012, pages 346-372.
For an abstract click here. A pdf version (306kB) is available.
M. Studeny, D. C. Haws: On polyhedral approximations of polytopes for learning Bayesian networks. Journal of Algebraic Statistics 4 (2013), pp. 58-91.
For an abstract click here. A pdf version of the published paper (827kB) is available.
M. Studeny: LP relaxations and pruning for characteristic imsets. Research report n. 2323, Institute of Information Theory and Automation, Prague, June 2012.
For an abstract click here. A pdf version (407kB) is available.
M. Studeny, D. Haws: Learning Bayesian network structure: towards the essential graph by integer linear programming tools. International Journal of Approximate Reasoning 55 (2014), pp. 1043-1071.
For an abstract click here. A pdf version of the published paper (477kB) is already open-access available.
M. Studeny: How matroids occur in the context of learning Bayesian network structure. In Uncertainty in Artificial Intelligence. Proceedings of the 31th Conference (M. Meila, T. Heskes eds.), AUAI Press, Corvallis 2015, pp. 832-841.
For an abstract click here. A pdf version (144kB) is available.
D. Haws, J. Cussens, M. Studeny: Polyhedral approaches to learning Bayesian networks. In Algebraic and Geometric Methods in Discrete Mathematics (H.A. Harrington, M. Omar, M. Wright eds.) series Contemporary Mathematics, volume 685, American Mathematical Society, 2017, pages 155-188. See doi:10.1090/conm/685/13751.
J. Cussens, D. Haws, M. Studeny: Polyhedral aspects of score equivalence in Bayesian network structure learning. Mathematical Programming A 164 (2017), n. 1/2, pp. 285-324. For an abstract click here. A pdf version of a preprint (415kB) is available.
Besides that, a full-text view-only version of the paper is also available.

Integer linear approach to learning decomposable models

M. Studeny, J. Cussens: The chordal graph polytope for learning decomposable models. In JMLR Workshops and Conference Proceedings 52 (2016), Proceedings of the Conference on Probabilistic Graphical Models [PGM 2016] (A. Antonucci, G. Corani, C. P. de Campos eds.), pp. 499-510. For an abstract click here. A pdf version of a preprint (253kB) is available.
M. Studeny, J. Cussens: Towards using the chordal graph polytope in learning decomposable models. International Journal of Approximate Reasoning 88 (2017), pp. 259-281. For an abstract click here. A pdf version of the published paper (557kB) is already open-access available.
M. Studeny, J. Cussens, V. Kratochvil: Dual formulation of the chordal graph conjecture. In Proceedings of Machine Learning Research 138 (2020), Proceedings of the International Conference on Probabilistic Graphical Models [PGM 2020], (M. Jaeger, T. D. Nielsen eds.), pp. 449-460. For an abstract click here. A pdf version (311kB) is available.
M. Studeny, J. Cussens, V. Kratochvil: The dual polyhedron to the chordal graph polytope and the rebuttal of the chordal graph conjecture. International Journal of Approximate Reasoning 138 (2021), pp. 188-203. For an abstract click here. A pdf version of a preprint (266kB) is available.

Other graphical approaches

M. Studeny: Comparison of graphical approaches to description of conditional independence structures. In Proceedings of WUPES`97, January 22-25, 1997, Prague, Czech Republic, pp. 156-172.
For an abstract click here. A pdf copy (converted postscript version) (222kB) is available.
A. Paz, R. Y. Geva and M. Studeny: Representation of irrelevance relations by annotated graphs. Fundamenta Informaticae 42 (2000), pp. 149-199.
For an abstract click here. A pdf copy (converted postscript version) (419kB) is available.

Marginal problem

M. Studeny: Marginal problem in different calculi of AI. In Advances in Intelligent Computing - IPMU'94 (B. Bouchon-Meunier, R. R. Yager, L. A. Zadeh eds.), Lecture Notes in Computer Science 945, Springer-Verlag, Berlin - Heidelberg 1995, pp. 348-359.
For an abstract click here. A pdf copy (converted postscript version) (219kB) is available.
M. Studeny: On marginalization, collapsibility and precollapsibility. In Distributions with Given Marginals and Moment Problems (V. Benes, J. Stepan eds.), Kluwer, Dordrecht 1997, pp. 191-198.
For an abstract click here. A pdf copy (converted postscript version) (162kB) is available.
A. Perez, M. Studeny: Comparison of two methods for approximation of probability distributions with prescribed marginals. Kybernetika 43 (2007), n. 5, pp. 591-618.
For an abstract click here. A pdf version of the published paper (462kB) is available.

Differentiation of measures

M. Studeny: Derivovani mer v metrickych prostorech. (in Czech, translation: differentiation of measures in metric spaces), graduate diploma thesis, Faculty of Mathematics and Physics, Charles University, Prague 1981, Czechoslovakia, 115 pages.
A pdf abstract (115kB) is available.
M. Studeny: On the differentiation theorem in metric groups. Commentationes Mathematicae Universitatis Carolinae 24 (1983), n. 2, pp. 223-232.
For an abstract click here. A scanned pdf copy (826kB) is available.

Other topics

M. Studeny: Convex cones in finite-dimensional real vector spaces. Kybernetika 29 (1993), n. 2, pp. 180-200. For an abstract click here. A pdf copy (converted postscript version) (272kB) is available.
P. Lachout, M. Studeny and J. Sindelar: On set-valued measures. Informatica 4 (1993), n. 1-2, pp. 21-44. For an abstract click here. A scanned pdf copy (8967kB) is available.