Intelligent tutoring systems by Bayesian nets with noisy gates

TL;DR

This paper addresses the challenge of building Bayesian-net–based ITSs while keeping the number of parameters manageable for real-time feedback. It introduces noisy gates (noisy-OR and noisy-AND) with a distinguished state to compact CPTs and derives a fast, linear-time updating scheme for posterior inferences. It also analyzes the semantics and monotonicity of gate parameters, and demonstrates two interaction patterns—Interchangeable Skills (Or) and Complementary Skills (And)—for modeling how learner skills affect question answers. The approach promises scalable, interpretable ITS models and points to extensions toward ordinal variables and credal nets for broader applicability, facilitating practical deployment in e-learning contexts.

Abstract

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.

Figures (2)

• Figure 1: An ITS to test multiplicative skills based on a BN.
• Figure 2: A noisy gate (explicit formulation).