Shubhendu Trivedi

Clustering students to generate an ensemble to improve standard test score predictions

In typical assessment student are not given feedback, as it is harder to predict student knowledge if it is changing during testing. Intelligent Tutoring systems, that offer assistance while the student is participating, offer a clear benefit of assisting students, but how well can they assess students? What is the trade off in terms of assessment accuracy if we allow student to be assisted on an exam. In a prior study, we showed the assistance with assessments quality to be equal. In this work, we introduce a more sophisticated method by which we can ensemble together multiple models based upon clustering students. We show that in fact, the assessment quality as determined by the assistance data is a better estimator of student knowledge. The implications of this study suggest that by using computer tutors for assessment, we can save much instructional time that is currently used for just assessment.

Clustered knowledge tracing

By learning a more distributed representation of the input space, clustering can be a powerful source of information for boosting the performance of predictive models. While such semi-supervised methods based on clustering have been applied to increase the accuracy of predictions of external tests, they have not yet been applied to improve within-tutor prediction of student responses. We use a widely adopted model for student prediction called knowledge tracing as our predictor and demonstrate how clustering students can improve model accuracy. The intuition behind this application of clustering is that different groups of students can be better fit with separate models. High performing students, for example, might be better modeled with a higher knowledge tracing learning rate parameter than lower performing students. We use a bagging method that exploits clusterings at different values for K in order to capture a variety of different categorizations of students. The method then combines the predictions of each cluster in order to produce a more accurate result than without clustering.

Predicting molecular properties with covariant compositional networks

Density functional theory (DFT) is the most successful and widely used approach for computing the electronic structure of matter. However, for tasks involving large sets of candidate molecules, running DFT separately for every possible compound of interest is forbiddingly expensive. In this paper, we propose a neural network based machine learning algorithm which, assuming a sufficiently large training sample of actual DFT results, can instead learn to predict certain properties of molecules purely from their molecular graphs. Our algorithm is based on the recently proposed covariant compositional networks framework and involves tensor reduction operations that are covariant with respect to permutations of the atoms. This new approach avoids some of the representational limitations of other neural networks that are popular in learning from molecular graphs and yields promising results in numerical experiments on the Harvard Clean Energy Project and QM9 molecular datasets.