This paper presents a machine learning approach to multidimensional item response theory (MIRT), a class of latent factor models that can be used to model and predict student performance from observed assessment data. Inspired by collaborative filtering, we define a general class of models that includes many MIRT models. We discuss the use of penalized joint maximum likelihood (JML) to estimate individual models and cross-validation to select the best performing model. This model evaluation process can be optimized using batching techniques, such that even sparse large-scale data can be analyzed efficiently. We illustrate our approach with simulated and real data, including an example from a massive open online course (MOOC). The high-dimensional model fit to this large and sparse dataset does not lend itself well to traditional methods of factor interpretation. By analogy to recommender-system applications, we propose an alternative "validation" of the factor model, using auxiliary information about the popularity of items consulted during an open-book exam in the course.

Factorization machines (FMs) are a powerful tool for regression and classification in the context of sparse observations, that has been successfully applied to collaborative filtering, especially when side information over users or items is available. Bayesian formulations of FMs have been proposed to provide confidence intervals over the predictions made by the model, however they usually involve Markov-chain Monte Carlo methods that require many samples to provide accurate predictions, resulting in slow training in the context of large-scale data. In this paper, we propose a variational formulation of factorization machines that allows us to derive a simple objective that can be easily optimized using standard mini-batch stochastic gradient descent, making it amenable to large-scale data. Our algorithm learns an approximate posterior distribution over the user and item parameters, which leads to confidence intervals over the predictions. We show, using several datasets, that it has comparable or better performance than existing methods in terms of prediction accuracy, and provide some applications in active learning strategies, e.g., preference elicitation techniques.

机构收集了大量的学习痕迹，但他们可能不会出于隐私问题披露它。合成数据生成为教育研究开辟了新的机会。在本文中，我们提出了一个可以保留参与者隐私的教育数据的生成模型，以及比较合成数据生成器的评估框架。我们展示了幼稚的假名如何导致重新识别威胁并提出保证隐私的技术。我们评估了现有大规模教育开放数据集的方法。