Cognitive modelling can discover the latent characteristics of examinees for predicting their performance (i.e. scores) on each problem. As cognitive modelling is important for numerous applications, e.g. personalized remedy recommendation, some solutions have been designed in the literature. However, the problem of extracting information from both objective and subjective problems to get more precise and interpretable cognitive analysis is still underexplored. To this end, we propose a fuzzy cognitive diagnosis framework (FuzzyCDF) for examinees' cognitive modelling with both objective and subjective problems. Specifically, to handle the partially correct responses on subjective problems, we first fuzzify the skill proficiency of examinees. Then, we combine fuzzy set theory and educational hypotheses to model the examinees' mastery on the problems. Further, we simulate the generation of examination scores by considering both slip and guess factors. Extensive experiments on three real-world datasets prove that FuzzyCDF can predict examinee performance more effectively, and the output of FuzzyCDF is also interpretative.

In Massively Open Online Courses (MOOCs) TA resources are limited; most MOOCs use peer assessments to grade assignments. Students have to divide up their time between working on their own homework and grading others. If there is no risk of being caught and penalized, students have no reason to spend any time grading others Course staff want to incentivize students to balance their time between course work and peer grading. They may do so by auditing students, ensuring that they perform grading correctly. One would not want students to invest too much time on peer grading, as this would result in poor course performance. We present the first model of strategic auditing in peer grading, modeling the student's choice of effort in response to a grader's audit levels as a Stackelberg game with multiple followers. We demonstrate that computing the equilibrium for this game is computationally hard. We then provide a PTAS in order to compute an approximate solution to the problem of allocating audit levels. However, we show that this allocation does not necessarily maximize social welfare; in fact, there exist settings where course auditor utility is arbitrarily far from optimal under an approximately optimal allocation. To circumvent this issue, we present a natural condition that guarantees that approximately optimal TA allocations guarantee approximately optimal welfare for the course auditors.

Parallel Test Paper Generation ( k -TPG) is a biobjective distributed resource allocation problem, which aims to generate multiple similarly optimal test papers automatically according to multiple user-specified criteria.Generating high-quality parallel test papers is challenging due to its NP-hardness in maximizing the collective objective functions.In this paper, we propose a Collective Biobjective Optimization (CBO) algorithm for solving k -TPG. CBO is a multi-step greedy-based approximation algorithm, which exploits the submodular property for biobjective optimization of k -TPG.Experiment results have shown that CBO has drastically outperformed the current techniques in terms of paper quality and runtime efficiency.

In this paper, we consider unregularized online learning algorithms in a Reproducing Kernel Hilbert Spaces (RKHS). Firstly, we derive explicit convergence rates of the unregularized online learning algorithms for classification associated with a general gamma-activating loss (see Definition 1 in the paper). Our results extend and refine the results in Ying and Pontil (2008) for the least-square loss and the recent result in Bach and Moulines (2011) for the loss function with a Lipschitz-continuous gradient. Moreover, we establish a very general condition on the step sizes which guarantees the convergence of the last iterate of such algorithms. Secondly, we establish, for the first time, the convergence of the unregularized pairwise learning algorithm with a general loss function and derive explicit rates under the assumption of polynomially decaying step sizes. Concrete examples are used to illustrate our main results. The main techniques are tools from convex analysis, refined inequalities of Gaussian averages, and an induction approach.

Students in a Massive Open Online Course (MOOC) interact with each other and the course staff through online discussion forums. While discussion forums play a central role in MOOCs, they also pose a challenge for instructors. The large number of student posts makes it difficult for an instructor to know where to intervene to answer questions, resolve issues, and provide feedback. In this work, we focus on automatically predicting speech acts in MOOC forum posts. Our speech act categories describe the purpose or function of the post in the ongoing discussion. Specifically, we address three main research questions. First, we investigate whether crowdsourced workers can reliably label MOOC forum posts using our speech act definitions. Second, we investigate whether our speech acts can help predict instructor interventions and assignment completion and performance. Finally, we investigate which types of features (derived from the post content, author, and surrounding context) are most effective for predicting our different speech act categories.

In this paper we propose a novel framework for decentralized, online learning by many learners. At each moment of time, an instance characterized by a certain context may arrive to each learner; based on the context, the learner can select one of its own actions (which gives a reward and provides information) or request assistance from another learner. In the latter case, the requester pays a cost and receives the reward but the provider learns the information. In our framework, learners are modeled as cooperative contextual bandits. Each learner seeks to maximize the expected reward from its arrivals, which involves trading off the reward received from its own actions, the information learned from its own actions, the reward received from the actions requested of others and the cost paid for these actions - taking into account what it has learned about the value of assistance from each other learner. We develop distributed online learning algorithms and provide analytic bounds to compare the efficiency of these with algorithms with the complete knowledge (oracle) benchmark (in which the expected reward of every action in every context is known by every learner). Our estimates show that regret - the loss incurred by the algorithm - is sublinear in time. Our theoretical framework can be used in many practical applications including Big Data mining, event detection in surveillance sensor networks and distributed online recommendation systems.

With the enormous scale of massive open online courses (MOOCs), peer grading is vital for addressing the assessment challenge for open-ended assignments or exams while at the same time providing students with an effective learning experience through involvement in the grading process. Most existing MOOC platforms use simple schemes for aggregating peer grades, e.g., taking the median or mean. To enhance these schemes, some recent research attempts have developed machine learning methods under either the cardinal setting (for absolute judgment) or the ordinal setting (for relative judgment). In this paper, we seek to study both cardinal and ordinal aspects of peer grading within a common framework. First, we propose novel extensions to some existing probabilistic graphical models for cardi- nal peer grading. Not only do these extensions give su- perior performance in cardinal evaluation, but they also outperform conventional ordinal models in ordinal eval- uation. Next, we combine cardinal and ordinal models by augmenting ordinal models with cardinal predictions as prior. Such combination can achieve further performance boosts in both cardinal and ordinal evaluations, suggesting a new research direction to pursue for peer grading on MOOCs. Extensive experiments have been conducted using real peer grading data from a course called “Science, Technology, and Society in China I” offered by HKUST on the Coursera platform.

Massive Open Online Courses (MOOCs) have received widespread attention for their potential to scale higher education, with multiple platforms such as Coursera, edX and Udacity recently appearing. Despite their successes, a major problem faced by MOOCs is low completion rates. In this paper, we explore the accurate early identification of students who are at risk of not completing courses. We build predictive models weekly, over multiple offerings of a course. Furthermore, we envision student interventions that present meaningful probabilities of failure, enacted only for marginal students.To be effective, predicted probabilities must be both well-calibrated and smoothed across weeks.Based on logistic regression, we propose two transfer learning algorithms to trade-off smoothness and accuracy by adding a regularization term to minimize the difference of failure probabilities between consecutive weeks. Experimental results on two offerings of a Coursera MOOC establish the effectiveness of our algorithms.

Increased interest in web-based education has spurred the proliferation of online learning environments. However, these platforms suffer from high dropout rates due to lack of sustained motivation among the students taking the course. In an effort to address this problem, we propose an incentive-based, instructor-driven approach to orchestrate the interactions in online educational forums (OEFs). Our approach takes into account the heterogeneity in skills among the students as well as the limited budget available to the instructor. We first analytically model OEFs in a non-strategic setting using ideas from lumpable continuous time Markov chains and compute expected aggregate transient net-rewards for the instructor and the students. We next consider a strategic setting where we use the rewards computed above to set up a mixed-integer linear program which views an OEF as a single-leader-multiple-followers Stackelberg game and recommends an optimal plan to the instructor for maximizing student participation. Our experimental results reveal several interesting phenomena including a striking non-monotonicity in the level of participation of students vis-a-vis the instructor's arrival rate.

We consider the problem of learning from revealed preferences in an online setting. In our framework, each period a consumer buys an optimal bundle of goods from a merchant according to her (linear) utility function and current prices, subject to a budget constraint. The merchant observes only the purchased goods, and seeks to adapt prices to optimize his profits. We give an efficient algorithm for the merchant's problem that consists of a learning phase in which the consumer's utility function is (perhaps partially) inferred, followed by a price optimization step. We also give an alternative online learning algorithm for the setting where prices are set exogenously, but the merchant would still like to predict the bundle that will be bought by the consumer, for purposes of inventory or supply chain management. In contrast with most prior work on the revealed preferences problem, we demonstrate that by making stronger assumptions on the form of utility functions, efficient algorithms for both learning and profit maximization are possible, even in adaptive, online settings.