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Personalization and active learning are key aspects to successful learning. These aspects are important to address in intelligent educational applications, as they help systems to adapt and close the gap between students with varying abilities, which becomes increasingly important in the context of online and distance learning. We run a comparative head-to-head study of learning outcomes for two popular online learning platforms: Platform A, which follows a traditional model delivering content over a series of lecture videos and multiple-choice quizzes, and Platform B, which creates a personalized learning environment and provides problem-solving exercises and personalized feedback. We report on the results of our study using pre- and post-assessment quizzes with participants taking courses on an introductory data science topic on two platforms. We observe a statistically significant increase in the learning outcomes on Platform B, highlighting the impact of well-designed and well-engineered technology supporting active learning and problem-based learning in online education. Moreover, the results of the self-assessment questionnaire, where participants reported on perceived learning gains, suggest that participants using Platform B improve their metacognition., Comment: 14 pages, 3 figures, 2 tables, accepted at AIED 2021 (2021 Conference on Artificial Intelligence in Education)

The choice of approximate posterior distributions plays a central role in stochastic variational inference (SVI). One effective solution is the use of normalizing flows \cut{defined on Euclidean spaces} to construct flexible posterior distributions. However, one key limitation of existing normalizing flows is that they are restricted to the Euclidean space and are ill-equipped to model data with an underlying hierarchical structure. To address this fundamental limitation, we present the first extension of normalizing flows to hyperbolic spaces. We first elevate normalizing flows to hyperbolic spaces using coupling transforms defined on the tangent bundle, termed Tangent Coupling ($\mathcal{TC}$). We further introduce Wrapped Hyperboloid Coupling ($\mathcal{W}\mathbb{H}C$), a fully invertible and learnable transformation that explicitly utilizes the geometric structure of hyperbolic spaces, allowing for expressive posteriors while being efficient to sample from. We demonstrate the efficacy of our novel normalizing flow over hyperbolic VAEs and Euclidean normalizing flows. Our approach achieves improved performance on density estimation, as well as reconstruction of real-world graph data, which exhibit a hierarchical structure. Finally, we show that our approach can be used to power a generative model over hierarchical data using hyperbolic latent variables., Comment: Preprint, work under review