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  1. Free, publicly-accessible full text available June 1, 2023
  2. Weinberger, Armin ; Chen, Wenli ; Hernández-Leo, Davinia ; & Chen, Bodong (Ed.)
    SimSnap responds to the need for a technology-based tool that supports learning at three social planes—individual, small group, and whole-class—while being easy to deploy with minimal technology overhead costs during their uptake. While much research has examined the efficacy of large-scale collaborative systems and individual-oriented learning systems, the intersection of and the movement between the three social planes is under explored. SimSnap is a cross-device, tablet-based platform that facilitates learning science concepts for middle school students through interactive simulations. Students in physical proximity can ‘snap’ their devices together to collaborate on learning activities. SimSnap enables real-time transition between individual and group activities in a classroom by offering reconfigurable simulations. SimSnap also provides an environment where open-ended and task-specific learning trajectories can be explored to maximize students’ learning potential. In this iteration of SimSnap, we have designed and implemented our first curriculum on SimSnap, focusing on plant biology, ecosystems, and genetics.
    Free, publicly-accessible full text available June 1, 2023
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  5. A modal decomposition is a useful tool that deconstructs the statistical dependence between two random variables by decomposing their joint distribution into orthogonal modes. Historically, modal decompositions have played important roles in statistics and information theory, e.g., in the study of maximal correlation. They are defined using the singular value decompo- sitions of divergence transition matrices (DTMs) and conditional expectation operators corresponding to joint distributions. In this paper, we first characterize the set of all DTMs, and illustrate how the associated conditional expectation operators are the only weak contractions among a class of natural candidates. While modal decompositions have several modern machine learning applications, such as feature extraction from categorical data, the sample complexity of estimating them in such scenarios has not been analyzed. Hence, we also establish some non-asymptotic sample complexity results for the problem of estimating dominant modes of an unknown joint distribution from training data.
  6. Stochastic gradient descent (SGD) and its variants have established themselves as the go-to algorithms for large-scale machine learning problems with independent samples due to their generalization performance and intrinsic computational advantage. However, the fact that the stochastic gradient is a biased estimator of the full gradient with correlated samples has led to the lack of theoretical understanding of how SGD behaves under correlated settings and hindered its use in such cases. In this paper, we focus on the Gaussian process (GP) and take a step forward towards breaking the barrier by proving minibatch SGD converges to a critical point of the full loss function, and recovers model hyperparameters with rate O(1/K) up to a statistical error term depending on the minibatch size. Numerical studies on both simulated and real datasets demonstrate that minibatch SGD has better generalization over state-of-the-art GP methods while reducing the computational burden and opening a new, previously unexplored, data size regime for GPs.
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