An augmented EM algorithm for monotonic Bayesian networks using parameterized conditional probability tables

Bayesian networks offer an attractive framework for describing the relationship between latent proficiency variables and observable outcomes. In educational applications, it is useful to restrict the conditional probability tables of the Bayesian network to be monotonic—increasing skill implies a high chance of a good performance. This paper describes the DiBello family of models for Bayesian networks, which enforce monotonicity, and introduces an augmented EM algorithm for estimating the parameters of these models. In a calibration experiment using simulated data, the algorithm did a good job recovering the model parameters and the conditional probability tables with sample sizes as low as 400.