Word embedding models learn semantically rich vector representations of words and are widely used to initialize natural processing language (NLP) models.The popular continuous bag-ofwords (CBOW) model of word2vec learns a vector embedding by masking a given word in a sentence and then using the other words as a context to predict it.A limitation of CBOW is that it equally weights the context words when making a prediction, which is inefficient, since some words have higher predictive value than others.We tackle this inefficiency by introducing the Attention Word Embedding (AWE) model, which integrates the attention mechanism into the CBOW model.We also propose AWE-S, which incorporates subword information.We demonstrate that AWE and AWE-S outperform the state-of-the-art word embedding models both on a variety of word similarity datasets and when used for initialization of NLP models.

This study examines fidelity of ranking and rating scales in the context of online peer review and assessment. Using the Monte-Carlo simulation technique, we demonstrated that rating scales outperform ranking scales in revealing the relative "true" latent quality of the peer-assessed artifacts via the observed aggregate peer assessment scores. Our analysis focused on a simple, single-round peer assessment process and took into account peer assessment network topology, network size, the number of assessments per artifact, and the correlation statistics used. This methodology allows to separate the effects of structural components of peer assessment from cognitive effects.

The ever growing amount of educational content renders it increasingly difficult to manually generate sufficient practice or quiz questions to accompany it. This paper introduces QG-Net, a recurrent neural network-based model specifically designed for automatically generating quiz questions from educational content such as textbooks. QG-Net, when trained on a publicly available, general-purpose question/answer dataset and without further fine-tuning, is capable of generating high quality questions from textbooks, where the content is significantly different from the training data. Indeed, QG-Net outperforms state-of-the-art neural network-based and rules-based systems for question generation, both when evaluated using standard benchmark datasets and when using human evaluators. QG-Net also scales favorably to applications with large amounts of educational content, since its performance improves with the amount of training data.

While computer and communication technologies have provided effective means to scale up many aspects of education, the submission and grading of assessments such as homework assignments and tests remains a weak link. In this paper, we study the problem of automatically grading the kinds of open response mathematical questions that figure prominently in STEM (science, technology, engineering, and mathematics) courses. Our data-driven framework for mathematical language processing (MLP) leverages solution data from a large number of learners to evaluate the correctness of their solutions, assign partial-credit scores, and provide feedback to each learner on the likely locations of any errors. MLP takes inspiration from the success of natural language processing for text data and comprises three main steps. First, we convert each solution to an open response mathematical question into a series of numerical features. Second, we cluster the features from several solutions to uncover the structures of correct, partially correct, and incorrect solutions. We develop two different clustering approaches, one that leverages generic clustering algorithms and one based on Bayesian nonparametrics. Third, we automatically grade the remaining (potentially large number of) solutions based on their assigned cluster and one instructor-provided grade per cluster. As a bonus, we can track the cluster assignment of each step of a multistep solution and determine when it departs from a cluster of correct solutions, which enables us to indicate the likely locations of errors to learners. We test and validate MLP on real-world MOOC data to demonstrate how it can substantially reduce the human effort required in large-scale educational platforms.

Advances in online and computer supported education afford exciting opportunities to revolutionize the classroom, while also presenting a number of new challenges not faced in traditional educational settings. Foremost among these challenges is the problem of accurately and efficiently evaluating learner work as the class size grows, which is directly related to the larger goal of providing quality, timely, and actionable formative feedback. Recently there has been a surge in interest in using peer grading methods coupled with machine learning to accurately and fairly evaluate learner work while alleviating the instructor bottleneck and grading overload. Prior work in peer grading almost exclusively focuses on numerically scored grades -- either real-valued or ordinal. In this work, we consider the implications of peer ranking in which learners rank a small subset of peer work from strongest to weakest, and propose new types of computational analyses that can be applied to this ranking data. We adopt a Bayesian approach to the ranked peer grading problem and develop a novel model and method for utilizing ranked peer-grading data. We additionally develop a novel procedure for adaptively identifying which work should be ranked by particular peers in order to dynamically resolve ambiguity in the data and rapidly resolve a clearer picture of learner performance. We showcase our results on both synthetic and several real-world educational datasets.

We develop a new model and algorithm for machine learning-based learning analytics, which estimate a learner's knowledge of the concepts underlying a domain. Our model represents the probability that a learner provides the correct response to a question in terms of three factors: their understanding of a set of underlying concepts, the concepts involved in each question, and each question's intrinsic difficulty. We estimate these factors given the graded responses to a set of questions. We develop a bi-convex algorithm to solve the resulting SPARse Factor Analysis (SPARFA) problem. We also incorporate user-defined tags on questions to facilitate the interpretability of the estimated factors. Experiments with synthetic and real-world data demonstrate the efficacy of our approach.

We introduce a novel analog-to-digital converter (ADC) based on the traditional successive approximation register. This architecture employs compressive sensing (CS) techniques to acquire and reconstruct frequency sparse signals. One important difference between our approach and traditional CS systems is that our architecture constrains the number of bits used during acquisition rather than the number of measurements. Our system is able to flexibly partition a fixed budget in order to trade the number of measurements it acquires with the quantization depth given to each measurement. We show that this degree of flexibility is particularly advantageous for ameliorating the CS noise folding phenomenon, allowing our ADC significant gains over measurement-constrained compressive sensing systems.

We consider the problem of recovering a matrix $\mathbf{M}$ that is the sum of a low-rank matrix $\mathbf{L}$ and a sparse matrix $\mathbf{S}$ from a small set of linear measurements of the form $\mathbf{y} = \mathcal{A}(\mathbf{M}) = \mathcal{A}({\bf L}+{\bf S})$. This model subsumes three important classes of signal recovery problems: compressive sensing, affine rank minimization, and robust principal component analysis. We propose a natural optimization problem for signal recovery under this model and develop a new greedy algorithm called SpaRCS to solve it. SpaRCS inherits a number of desirable properties from the state-of-the-art CoSaMP and ADMiRA algorithms, including exponential convergence and efficient implementation. Simulation results with video compressive sensing, hyperspectral imaging, and robust matrix completion data sets demonstrate both the accuracy and efficacy of the algorithm.

We consider bearing estimation of multiple narrow-band plane waves impinging on an array of sensors. For this problem, bearing estimation algorithms such as minimum variance distortionless response (MVDR), multiple signal classification, and maximum likelihood generally require the array covariance matrix as sufficient statistics. Interestingly, the rank of the array covariance matrix is approximately equal to the number of the sources, which is typically much smaller than the number of sensors in many practical scenarios. In these scenarios, the covariance matrix is low-rank and can be estimated via matrix completion from only a small subset of its entries. We propose a distributed matrix completion framework to drastically reduce the inter-sensor communication in a network while still achieving near-optimal bearing estimation accuracy. Using recent results in noisy matrix completion, we provide sampling bounds and show how the additive noise at the sensor observations affects the reconstruction performance. We demonstrate via simulations that our approach sports desirable tradeoffs between communication costs and bearing estimation accuracy.