Summary: In this paper we study the problem of student knowledge level estimation. We use probabilistic models learned from collected data to model the tested students. We propose and compare experimentally several different Bayesian network models for the score prediction of student’s knowledge. The proposed scoring algorithm provides not only the expected value of the total score but the whole probability distribution of the total score. This means that confidence intervals of predicted total score can be provided along the expected value. The key that enabled efficient computations with the studied models is a newly proposed inference algorithm based on the CP tensor decomposition, which is used for the computation of the score distribution. The proposed algorithm is two orders of magnitude faster than a state of the art method. We report results of experimental comparisons on a large dataset from the Czech National Graduation Exam in Mathematics. In this evaluation the best performing model is an IRT model with one continuous normally distributed skill variable related to all items by the graded response models. The second best is a multidimensional IRT model with an expert structure of items-skills relations and a covariance matrix for the skills. This model has a higher improvement with larger training sets and seems to be the model of choice if a sufficiently large training dataset is available.
For the entire collection see [Zbl 1487.68022].