The prevalence of e-learning systems and on-line courses has made educational material widely accessible to students of varying abilities and backgrounds. There is thus a growing need to accommodate for individual differences in e-learning systems. This paper presents an algorithm called Edu-Rank for personalizing educational content to students that combines a collaborative filtering algorithm with voting methods. EduRank constructs a difficulty ranking for each student by aggregating the rankings of similar students using different aspects of their performance on common questions. These aspects include grades, number of retries, and time spent solving questions. It infers a difficulty ranking directly over the questions for each student, rather than ordering them according to the student's predicted score. The EduRank algorithm was tested on two data sets containing thousands of students and a million records. It was able to outperform the state-ofthe-art ranking approaches as well as a domain expert. EduRank was used by students in a classroom activity, where a prior model was incorporated to predict the difficulty rankings of students with no prior history in the system. It was shown to lead students to solve more difficult questions than an ordering by a domain expert, without reducing their performance.
As e-learning systems become more prevalent, there is a growing need for them to accommodate individual differences between students. This paper addresses the problem of how to personalize educational content to students in order to maximize their learning gains over time. We present a new computational approach to this problem called MAPLE (Multi-Armed Bandits based Personalization for Learning Environments) that combines difficulty ranking with multiarmed bandits. Given a set of target questions MAPLE estimates the expected learning gains for each question and uses an exploration-exploitation strategy to choose the next question to pose to the student. It maintains a personalized ranking over the difficulties of question in the target set which is used in two ways: First, to obtain initial estimates over the learning gains for the set of questions. Second, to update the estimates over time based on the students responses. We show in simulations that MAPLE was able to improve students' learning gains compared to approaches that sequence questions in increasing level of difficulty, or rely on content experts. When implemented in a live e-learning system in the wild, MAPLE showed promising results. This work demonstrates the efficacy of using stochastic approaches to the sequencing problem when augmented with information about question difficulty.
We propose a novel way to incorporate expert knowledge into the training of deep neural networks. Many approaches encode domain constraints directly into the network architecture, requiring non-trivial or domain-specific engineering. In contrast, our approach, called MultiplexNet, represents domain knowledge as a quantifier-free logical formula in disjunctive normal form (DNF) which is easy to encode and to elicit from human experts. It introduces a latent Categorical variable that learns to choose which constraint term optimizes the error function of the network and it compiles the constraints directly into the output of existing learning algorithms. We demonstrate the efficacy of this approach empirically on several classical deep learning tasks, such as density estimation and classification in both supervised and unsupervised settings where prior knowledge about the domains was expressed as logical constraints. Our results show that the MultiplexNet approach learned to approximate unknown distributions well, often requiring fewer data samples than the alternative approaches. In some cases, MultiplexNet finds better solutions than the baselines; or solutions that could not be achieved with the alternative approaches. Our contribution is in encoding domain knowledge in a way that facilitates inference. We specifically focus on quantifier-free logical formulae that are specified over the output domain of a network. We show that this approach is both efficient and general; and critically, our approach guarantees 100% constraint satisfaction in a network's output.
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