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.
翻译:在医学成像和数字营销等现代应用中,火标正在日益流行。 在本文中,我们提出一个稀疏的 高温添加回归(STAR), 以星标反应为模型, 将之作为高温共变的灵活非参数函数。 拟议的模型有效地利用了高温叠加回归中的稀疏和低级结构。 我们把参数估计作为一个非碳化优化问题来制定, 并提议一个有效的、 惩罚性的交替最小化算法。 我们为从每个迭代中获取的估算算法设定了一个非物质错误, 它揭示了优化错误与统计趋同率之间的相互作用。 我们通过广泛的比较模拟研究以及在线广告中点击通速预测的应用, 展示了STAR的功效。