Topical Hidden Markov Models for Skill Discovery in Tutorial Data

Jose P. Gonzalez-Brenes

Language Technologies Institute, Carnegie Mellon University Pittsburgh, PA 15213 USA

Jack Mostow

Language Technologies Institute, Carnegie Mellon University Pittsburgh, PA 15213 USA


The rst step for an Intelligent Tutoring Sys- tem to adapt teaching is inferring students' understanding of the subject matter (Van- Lehn, 1988). Existing automatic approaches for inferring students' knowledge requires a cognitive model { the mapping between the tutor problems and the set of skills required. This is a very expensive requirement, since it often depends on expert domain knowledge (Beck, 2007).

The success of previous methods for auto- matic construction of cognitive models has been limited (Desmarais, 2011). Previous work on inferring students' knowledge from temporal data has relied on expert annota- tors to nd the grouping of problems into skills (Gonzalez-Brenes & Mostow, 2012). For example, matrix-based methods (Winters et al., 2005), such as Principal Component Analysis, Non-Negative Matrix Factorization and the Q-Matrix Method (Barnes, 2005) ig- nore the temporal dimension of the data. On the other hand, Learning Factors Anal- ysis (Cen et al., 2006) is designed for tem- poral data, but still requires expert's anno- tations. Our goal is a data-driven approach to model students' time varying knowledge, without requiring expert annotation of the skills needed by the students.

Our proposed model, Topical Hidden Markov Model (HMM), uses an input sequence to model the order in which students solve prob- lems, and an output sequence to model stu- dents' performance on the problems they solve. We propose a Gibbs Sampling algo-

rithm that infers a factorization of problems into skills, and estimates the student knowl- edge of the skills across time. We validate our approach with data collected with the Bridge to Algebra Cognitive Tutor R (Koedinger et al., 2010).


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