Knowledge tracing (KT) refers to the problem of predicting future learner performance given their past performance in educational applications. Recent developments in KT using flexible deep neural network-based models excel at this task. However, these models often offer limited interpretability, thus making them insufficient for personalized learning, which requires using interpretable feedback and actionable recommendations to help learners achieve better learning outcomes. In this paper, we propose attentive knowledge tracing (AKT), which couples flexible attention-based neural network models with a series of novel, interpretable model components inspired by cognitive and psychometric models. AKT uses a novel monotonic attention mechanism that relates a learner's future responses to assessment questions to their past responses; attention weights are computed using exponential decay and a context-aware relative distance measure, in addition to the similarity between questions. Moreover, we use the Rasch model to regularize the concept and question embeddings; these embeddings are able to capture individual differences among questions on the same concept without using an excessive number of parameters. We conduct experiments on several real-world benchmark datasets and show that AKT outperforms existing KT methods (by up to 6% in AUC in some cases) on predicting future learner responses. We also conduct several case studies and show that AKT exhibits excellent interpretability and thus has potential for automated feedback and personalization in real-world educational settings.

This paper deals with the recovery of an unknown, lowrank matrix from quantized and (possibly) corrupted measurements of a subset of its entries. We develop statistical models and corresponding (multi-)convex optimization algorithms for quantized matrix completion (Q-MC) and quantized robust principal component analysis (Q-RPCA). In order to take into account the quantized nature of the available data, we jointly learn the underlying quantization bin boundaries and recover the low-rank matrix, while removing potential (sparse) corruptions. Experimental results on synthetic and two real-world collaborative filtering datasets demonstrate that directly operating with the quantized measurements-rather than treating them as real values-results in (often significantly) lower recovery error if the number of quantization bins is less than about 10.

We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for educational applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA) that jointly traces learner concept knowledge over time, analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc., or the forgetting effect), and estimates the content organization and difficulty of the questions in assessments. These quantities are estimated solely from binary-valued (correct/incorrect) graded learner response data and the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instant. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, analyzing the quality and content organization of learning resources, and estimating the question-concept associations and the question difficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses compared to existing collaborative filtering and knowledge tracing methods.

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