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作者：Li, Runze; Li, Weiming; Wang, Qinwen
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Shanghai University of Finance & Economics; Fudan University
摘要：Tyler's M estimator, as a robust alternative to the sample covariance matrix, has been widely applied in robust statistics. However, classical theory on Tyler's M estimator is mainly developed in the low-dimensional regime for elliptical populations. It remains largely unknown when the parameter of dimension p grows proportionally to the sample size n for general populations. By using the eigenvalues of Tyler's M estimator, this article develops tests for the identity and equality of shape mat...
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作者：Zhou, Jie; Hao, Botao; Wen, Zheng; Zhang, Jingfei; Sun, Will Wei
作者单位：Amazon.com; Alphabet Inc.; DeepMind; Emory University; Purdue University System; Purdue University
摘要：Multi-dimensional online decision making plays a crucial role in many real applications such as online recommendation and digital marketing. In these problems, a decision at each time is a combination of choices from different types of entities. To solve it, we introduce stochastic low-rank tensor bandits, a class of bandits whose mean rewards can be represented as a low-rank tensor. We consider two settings, tensor bandits without context and tensor bandits with context. In the first setting,...
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作者：Chen, Yang
作者单位：University of Michigan System; University of Michigan
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作者：Leiner, James; Duan, Boyan; Wasserman, Larry; Ramdas, Aaditya
作者单位：Carnegie Mellon University; Carnegie Mellon University; Alphabet Inc.; Google Incorporated
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作者：Furfaro, Emanuela
作者单位：University of Washington; University of Washington Seattle
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作者：Zhang, Shucong; Wang, Huiyuan; Lin, Wei
作者单位：University of International Business & Economics; University of Pennsylvania; Peking University; Peking University
摘要：High-dimensional compositional data are prevalent in many applications. The simplex constraint poses intrinsic challenges to inferring the conditional dependence relationships among the components forming a composition, as encoded by a large precision matrix. We introduce a precise specification of the compositional precision matrix and relate it to its basis counterpart, which is shown to be asymptotically identifiable under suitable sparsity assumptions. By exploiting this connection, we pro...
