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Zhou, Le; Wang, Boxiang; Zou, Hui (, Journal of the American Statistical Association)
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Wang, Boxiang; Zou, Hui (, Technometrics)
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Hao, Botao; Wang, Boxiang; Wang, Pengyuan; Zhang, Jingfei; Yang, Jian; Sun, Will Wei (, Journal of machine learning research)null (Ed.)Tensors are becoming prevalent in modern applications such as medical imaging and digital marketing. In this paper, we propose a sparse tensor additive regression (STAR) that models a scalar response as a flexible nonparametric function of tensor covariates. The proposed model effectively exploits the sparse and low-rank structures in the tensor additive regression. We formulate the parameter estimation as a non-convex optimization problem, and propose an efficient penalized alternating minimization algorithm. We establish a non-asymptotic error bound for the estimator obtained from each iteration of the proposed algorithm, which reveals an interplay between the optimization error and the statistical rate of convergence. We demonstrate the efficacy of STAR through extensive comparative simulation studies, and an application to the click-through-rate prediction in online advertising.more » « less
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Wang, Boxiang; Zou, Hui (, Stat)Many machine learning models have tuning parameters to be determined by the training data, and cross‐validation (CV) is perhaps the most commonly used method for selecting tuning parameters. This work concerns the problem of estimating the generalization error of a CV‐tuned predictive model. We propose to use an honest leave‐one‐out cross‐validation framework to produce a nearly unbiased estimator of the post‐tuning generalization error. By using the kernel support vector machine and the kernel logistic regression as examples, we demonstrate that the honest leave‐one‐out cross‐validation has very competitive performance even when competing with the state‐of‐the‐art .632+ estimator.more » « less
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