On Identifiability of BN2A Networks

0578481 - ÚTIA 2024 RIV CH eng C - Konferenční příspěvek (zahraniční konf.)
Pérez Cabrera, Iván - Vomlel, Jiří
On Identifiability of BN2A Networks.
Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2023.. Cham: Springer, 2023 - (Bouraoui, Z.; Vesic, S.), s. 136-148. Lecture Notes in Computer Science, Lecture Notes in Artificial Intelligence, 14294. ISBN 978-3-031-45607-7.
[European Conference, ECSQARU 2023 /17./. Arras (FR), 19.09.2023-22.09.2023]
Grant CEP: GA ČR(CZ) GA21-03658S; GA ČR(CZ) GA22-11101S
Institucionální podpora: RVO:67985556
Klíčová slova: Bayesian networks * BN2A networks * Cognitive Diagnostic Modeling * Psychometrics * Model Identifiability
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
http://library.utia.cas.cz/separaty/2023/MTR/vomlel-0578481.pdf

In this paper, we consider two-layer Bayesian networks. The first layer consists of hidden (unobservable) variables and the second layer consists of observed variables. All variables are assumed to be binary. The variables in the second layer depend on the variables in the first layer. The dependence is characterised by conditional probability tables representing Noisy-AND or simple Noisy-AND. We will refer to this class of models as BN2A models. We found that the models known in the Bayesian network community as Noisy-AND and simple Noisy-AND are also used in the cognitive diagnostic modelling known in the psychometric community under the names of RRUM and DINA, respectively. In this domain, the hidden variables of BN2A models correspond to skills and the observed variables to students’ responses to test questions. In this paper we analyse the identifiability of these models. Identifiability is an important concept because without it we cannot hope to learn correct models. We present necessary conditions for the identifiability of BN2As with Noisy-AND models. We also propose and test a numerical approach for testing identifiability.
Trvalý link: https://hdl.handle.net/11104/0347648