Dynamic Knowledge embedding and tracing

The goal of knowledge tracing is to track the state of a student's knowledge as it evolves over time. This plays a fundamental role in understanding the learning process and is a key task in the development of an intelligent tutoring system. In this paper we propose a novel approach to knowledge tracing that combines techniques from matrix factorization with recent progress in recurrent neural networks (RNNs) to effectively track the state of a student's knowledge. The proposed \emph{DynEmb} framework enables the tracking of student knowledge even without the concept/skill tag information that other knowledge tracing models require while simultaneously achieving superior performance. We provide experimental evaluations demonstrating that DynEmb achieves improved performance compared to baselines and illustrating the robustness and effectiveness of the proposed framework. We also evaluate our approach using several real-world datasets showing that the proposed model outperforms the previous state-of-the-art. These results suggest that combining embedding models with sequential models such as RNNs is a promising new direction for knowledge tracing.

Dynamic matrix recovery from incomplete observations under an exact low-rank constraint

Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by incorporating temporal information and allowing for the possibility of time-varying models, significant improvements are possible in practice. However, despite the reported superior empirical performance of these dynamic models over their static counterparts, there is limited theoretical justification for introducing these more complex models. In this paper we aim to address this gap by studying the problem of recovering a dynamically evolving low-rank matrix from incomplete observations. First, we propose the locally weighted matrix smoothing (LOWEMS) framework as one possible approach to dynamic matrix recovery. We then establish error bounds for LOWEMS in both the {\em matrix sensing} and {\em matrix completion} observation models. Our results quantify the potential benefits of exploiting dynamic constraints both in terms of recovery accuracy and sample complexity. To illustrate these benefits we provide both synthetic and real-world experimental results.