Sparse Tensor Additive Regression
Sparse Tensor Additive Regression
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发表时间：
2019-03
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通讯作者：
Botao Hao;Boxiang Wang;Pengyuan Wang;Jingfei Zhang;Jian Yang;W. Sun
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作者：
Botao Hao;Boxiang Wang;Pengyuan Wang;Jingfei Zhang;Jian Yang;W. Sun
张量在医学成像和数字营销等现代应用中越来越普遍。本文提出了一种稀疏张量加性回归（STAR），它将标量响应建模为张量协变量的柔性非参数函数。该模型有效地利用了张量加性回归中的稀疏和低秩结构。我们将参数估计表述为一个非凸优化问题，并提出了一种有效的惩罚交替最小化算法。我们为算法每次迭代得到的估计量建立了一个非渐近误差界，揭示了优化误差与统计收敛速度之间的相互作用。我们通过广泛的比较模拟研究证明了STAR的有效性，并将其应用于在线广告的点击率预测。
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.