Seminar in Psychometrics
Probabilistic Graphical Models for Computerized Adaptive Testing
Speaker: Iván Leonardo Pérez Cabrera (Charles University, ÚTIA & ICS CAS)
Date and time: Thursday, April 2, 2026 (16:00 PM CET)
Place ICS CAS room 318, Pod Vodárenskou věží 2, Prague 8, also on Zoom.
Zoom: 949 6153 1717, passcode: 646735.
Bayesian networks (BNs), a family of probabilistic graphical models, have been successfully applied in educational assessment. This presentation focuses on BN2A models, a specialized class of bipartite BNs where hidden binary variables (skills) in the first layer influence observed binary variables (item responses) in the second layer through Noisy-AND conditional probability tables. These canonical models in the BN literature correspond to well-known cognitive diagnostic models (CDMs) in psychometrics: Leak Noisy-AND is equivalent to the Reduced Reparametrized Unified Model (RRUM), and Simple Noisy-AND corresponds to the Deterministic Input Noisy AND (DINA) model. BN2A models enable fine-grained skill classification, making them particularly valuable for computerized adaptive testing (CAT). While traditional CAT relies on unidimensional Item Response Theory (IRT) models, cognitive diagnostic CAT (CD-CAT) combines adaptive efficiency with detailed diagnostic feedback about skill mastery patterns. In particular, we focus on Noisy-AND CAT as a specific implementation of CD-CAT. This talk presents doctoral research on BN2A models, covering four key contributions: (1) characterization of monotonicity properties, (2) numerical identifiability conditions, (3) parameter and structure learning through an EM algorithm and non-negative Restricted Boltzmann Machines, and (4) a comprehensive comparison of item selection algorithms (PWKL, Shannon Entropy, Mutual Information) for Noisy-AND CAT. For this last contribution, our simulation results reveal that when item parameters and prior distributions are properly calibrated, different models and item selection algorithms achieve statistically equivalent classification accuracy, providing practitioners with flexibility in implementation choices.
References:Pérez, I., & Vomlel, J. (2022, May). On the rank of 2×2×2 probability tables. In A. Salmerón & R. Rumí (Eds.), Proceedings of the 11th international conference on probabilistic graphical models (pp. 361–372, Vol. 186). PMLR. proceedings.mlr.press
Pérez, I., & Vomlel, J. (2023). On identifiability of BN2A networks. Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 17th European Conference, ECSQARU 2023, Arras, France, September 19–22, 2023, Proceedings, 136–148. doi.org/10.1007/978-3-031-45608-4_11
Pérez, I., & Vomlel, J. (2025) Structural Learning of BN2A models, Proceedings of the 13th Workshop on Uncertainty Processing (WUPES’25), p. 176-187, Eds: Studený Milan, Ay Nihat, Capotorti Andrea, Csirmaz László, Jiroušek Radim, Kleiter Gernot D., Shenoy Prakash P. proceedings
Pérez, I., & Vomlel, J., & Martinková P. (2025) From RBMs to BN2A Models: Parameter Transformation for Interpretable Educational Diagnostics, Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2025 Proceedings, p. 104-117, Eds: Sauerwald K., Thimm M. doi.org/10.1007/978-3-032-05134-9_8