We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model represents the signal tensor of interest using a series of structured sign tensors. Unlike earlier methods, the sign series representation effectively addresses both low- and high-rank signals, while encompassing many existing tensor models -- including CP models, Tucker models, single index models, several hypergraphon models -- as special cases. We show that the sign tensor series is theoretically characterized, and computationally estimable, via classification tasks with carefully-specified weights. Excess risk bounds, estimation error rates, and sample complexities are established. We demonstrate the outperformance of our approach over previous methods on two datasets, one on human brain connectivity networks and the other on topic data mining.
Near-Linear Time Local Polynomial Nonparametric Estimation with Box Kernels
Warrington College of Business, University of Florida（佛罗里达大学沃顿商学院）；Institute of Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Paul G. Allen School of Computer Science and Engineering, University of Washington（华盛顿大学保罗·G·艾伦计算机科学与工程学院）
局部多项式回归（Fan and Gijbels 1996）是非参数密度估计和回归问题的一类重要方法。然而，局部多项式回归的直接实现具有二次时间复杂度，这阻碍了其在大规模数据分析中的适用性。在本文中，我们显着加速计算的本地多项式估计的新应用程序的多维二进制索引树（Fenwick 1994）。该算法的时间复杂度和空间复杂度与输入数据点的个数近似成线性关系。仿真结果证实了我们所提出的方法的效率和有效性。
Detecting Stochasticity in Discrete Signals via Nonparametric Excursion Theorem
Dept. of Mechanical Engineering, Michigan State University（密歇根州立大学机械工程系）；Dept. of Computational Mathematics, Science and Engineering, Michigan State University（密歇根州立大学计算数学、科学与工程系）
