Monotonicity in Bayesian Networks for Computerized Adaptive Testing

  • Martin PlajnerEmail author
  • Jiří Vomlel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)


Artificial intelligence is present in many modern computer science applications. The question of effectively learning parameters of such models even with small data samples is still very active. It turns out that restricting conditional probabilities of a probabilistic model by monotonicity conditions might be useful in certain situations. Moreover, in some cases, the modeled reality requires these conditions to hold. In this article we focus on monotonicity conditions in Bayesian Network models. We present an algorithm for learning model parameters, which satisfy monotonicity conditions, based on gradient descent optimization. We test the proposed method on two data sets. One set is synthetic and the other is formed by real data collected for computerized adaptive testing. We compare obtained results with the isotonic regression EM method by Masegosa et al. which also learns BN model parameters satisfying monotonicity. A comparison is performed also with the standard unrestricted EM algorithm for BN learning. Obtained experimental results in our experiments clearly justify monotonicity restrictions. As a consequence of monotonicity requirements, resulting models better fit data.


Computerized adaptive testing Monotonicity Isotonic regression EM Gradient method Parameters learning 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University, PraguePragueCzech Republic
  2. 2.Institute of Information Theory and AutomationCzech Academy of SciencesPrague 8Czech Republic

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