0639050 20251006140507.320250918235959.9 12 s. P cav_un_epca*0636591978-80-7378-525-3176-187PragueMatfyzPress2025StudenýMilanAyNihatCapotortiAndreaCsirmazLászlóJiroušekRadimKleiterGernot D.ShenoyPrakash P. Bayesian networks Psychometrical models Noisy-AND models cav_un_auth*0458433 Pérez Cabrera Iván UTIA-B Zpracování signálů Department of Signal Processing ZS ZS MX Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101228 Vomlel Jiří UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. https://library.utia.cas.cz/separaty/2025/MTR/vomlel-0639050.pdf Bayesian networks are a popular framework for modeling probabilistic relationships between random variables and have been used successfully in educational tests. There is interest in a particular type of Bayesian networks we have called BN2A, which are characterized as bipartite networks, where the first layer consists of hidden variables (which commonly represent skills) and the second layer consists of observed variables (which represent questions in a test). In BN2A models all variables are assumed to be binary. The variables in the second layer depend on the variables in the first layer and this dependence is characterized by conditional probability tables representing Noisy-AND models. In this work, we propose an Expectation-Maximization (EM) algorithm for learning the structure of BN2A models, that is, for learning the relationship between hidden variables and observed variables. To test the structural learning algorithm, we conducted two experiments. For the first experiment, we used synthetic data generated from a BN2A model that we previously defined, while for the second experiment we used a well-known real-world dataset in the field of Cognitive Diagnostic Models, the Fraction Subtraction dataset. Our proposed algorithm has interesting potential use cases. One key application is to generate a reasonably accurate BN2A structure model for educational diagnosis, particularly in scenarios where no prior model exists. Depending on the required level of accuracy, the estimated model can be used directly to analyze skill profiles or serve as an initial framework for test designers, who can further refine it before implementation. cav_un_auth*0493361 Workshop on Uncertainty Processing (WUPES’25) 20250604 20250607 Třešť CZ JD 10000 10200 10201 2026 2 PR RVO:67985556 https://hdl.handle.net/11104/0370050 cav_un_auth*0363021 Faculty of Mathematics and Physics, Charles University Prague, Sokolovská 83,186 75 Praha, Czech Republic CZ S 2025 SCOPUS PUBMED WOS cav_un_epca*0636591 Proceedings of the 13th Workshop on Uncertainty Processing (WUPES’25) 978-80-7378-525-3 176 187 Prague MatfyzPress 2025 719 Studený Milan 340 Ay Nihat 340 Capotorti Andrea 340 Csirmaz László 340 Jiroušek Radim 340 Kleiter Gernot D. 340 Shenoy Prakash P. 340