Intelligent tutoring systems by Bayesian nets with noisy gates

Directed graphical models such as Bayesian nets are often used to implement intelligent tutoring systems able to interact in real-time with learners in a purely automatic way. When coping with such models, keeping a bound on the number of parameters might be important for multiple reasons. First, as these models are typically based on expert knowledge, a huge number of parameters to elicit might discourage practitioners from adopting them. Moreover, the number of model parameters affects the complexity of the inferences, while a fast computation of the queries is needed for real-time feedback. We advocate logical gates with uncertainty for a compact parametrization of the conditional probability tables in the underlying Bayesian net used by tutoring systems. We discuss the semantics of the model parameters to elicit and the assumptions required to apply such approach in this domain. We also derive a dedicated inference scheme to speed up computations.

Rubric-based Learner Modelling via Noisy Gates Bayesian Networks for Computational Thinking Skills Assessment

In modern and personalised education, there is a growing interest in developing learners' competencies and accurately assessing them. In a previous work, we proposed a procedure for deriving a learner model for automatic skill assessment from a task-specific competence rubric, thus simplifying the implementation of automated assessment tools. The previous approach, however, suffered two main limitations: (i) the ordering between competencies defined by the assessment rubric was only indirectly modelled; (ii) supplementary skills, not under assessment but necessary for accomplishing the task, were not included in the model. In this work, we address issue (i) by introducing dummy observed nodes, strictly enforcing the skills ordering without changing the network's structure. In contrast, for point (ii), we design a network with two layers of gates, one performing disjunctive operations by noisy-OR gates and the other conjunctive operations through logical ANDs. Such changes improve the model outcomes' coherence and the modelling tool's flexibility without compromising the model's compact parametrisation, interpretability and simple experts' elicitation. We used this approach to develop a learner model for Computational Thinking (CT) skills assessment. The CT-cube skills assessment framework and the Cross Array Task (CAT) are used to exemplify it and demonstrate its feasibility.

Modelling Assessment Rubrics through Bayesian Networks: a Pragmatic Approach

Automatic assessment of learner competencies is a fundamental task in intelligent tutoring systems. An assessment rubric typically and effectively describes relevant competencies and competence levels. This paper presents an approach to deriving a learner model directly from an assessment rubric defining some (partial) ordering of competence levels. The model is based on Bayesian networks and exploits logical gates with uncertainty (often referred to as noisy gates) to reduce the number of parameters of the model, so to simplify their elicitation by experts and allow real-time inference in intelligent tutoring systems. We illustrate how the approach can be applied to automatize the human assessment of an activity developed for testing computational thinking skills. The simple elicitation of the model starting from the assessment rubric opens up the possibility of quickly automating the assessment of several tasks, making them more easily exploitable in the context of adaptive assessment tools and intelligent tutoring systems.

ADAPQUEST: A Software for Web-Based Adaptive Questionnaires based on Bayesian Networks

We introduce ADAPQUEST, a software tool written in Java for the development of adaptive questionnaires based on Bayesian networks. Adaptiveness is intended here as the dynamical choice of the question sequence on the basis of an evolving model of the skill level of the test taker. Bayesian networks offer a flexible and highly interpretable framework to describe such testing process, especially when coping with multiple skills. ADAPQUEST embeds dedicated elicitation strategies to simplify the elicitation of the questionnaire parameters. An application of this tool for the diagnosis of mental disorders is also discussed together with some implementation details.

A New Score for Adaptive Tests in Bayesian and Credal Networks

A test is adaptive when its sequence and number of questions is dynamically tuned on the basis of the estimated skills of the taker. Graphical models, such as Bayesian networks, are used for adaptive tests as they allow to model the uncertainty about the questions and the skills in an explainable fashion, especially when coping with multiple skills. A better elicitation of the uncertainty in the question/skills relations can be achieved by interval probabilities. This turns the model into a credal network, thus making more challenging the inferential complexity of the queries required to select questions. This is especially the case for the information theoretic quantities used as scores to drive the adaptive mechanism. We present an alternative family of scores, based on the mode of the posterior probabilities, and hence easier to explain. This makes considerably simpler the evaluation in the credal case, without significantly affecting the quality of the adaptive process. Numerical tests on synthetic and real-world data are used to support this claim.