32,149 research outputs found

    The Power of Giving Feedback and Receiving Feedback in Peer Assessment

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    Despite well-documented promises of peer assessment, it is still unclear how peer as-sessment works and what contributes to students\u2019 learning gains. In order to identify cognitive processes that lead to learning enhancement, this study examined 41 stu-dents\u2019 responses to online surveys and also their online written interactions when they participated in a peer assessment activity. Data analysis revealed that students were en-gaged in various learning processes in the phases of giving and receiving feedback. While students acknowledged that both phases contributed to their learning, a greater number of students indicated that they perceived more learning benefits from giving feedback rather than receiving feedback. Interpretations and implications were dis-cussed

    Calibrating nonconvex penalized regression in ultra-high dimension

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    We investigate high-dimensional nonconvex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is nonunique and is not guaranteed to contain the oracle estimator; (2) even if a solution path is known to contain the oracle estimator, the optimal tuning parameter depends on many unknown factors and is hard to estimate. To address these two challenging issues, we first prove that an easy-to-calculate calibrated CCCP algorithm produces a consistent solution path which contains the oracle estimator with probability approaching one. Furthermore, we propose a high-dimensional BIC criterion and show that it can be applied to the solution path to select the optimal tuning parameter which asymptotically identifies the oracle estimator. The theory for a general class of nonconvex penalties in the ultra-high dimensional setup is established when the random errors follow the sub-Gaussian distribution. Monte Carlo studies confirm that the calibrated CCCP algorithm combined with the proposed high-dimensional BIC has desirable performance in identifying the underlying sparsity pattern for high-dimensional data analysis.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1159 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org
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