论文标题
零截断的泊松回归，用于稀疏的多路计数数据被false Zeros损坏
Zero-Truncated Poisson Regression for Sparse Multiway Count Data Corrupted by False Zeros
论文作者
论文摘要
我们为多路计数数据提出了一种新型的统计推理方法，该方法被错误的零零损坏，这些零与真实的零计数无法区分。我们的方法包括零截断的泊松分布以忽略所有零值。这种简单的截断方法消除了区分真实和虚假零计数并减少要处理的数据量的需求。推理是通过张量完成来完成的，该张量将低级张量结构施加在泊松参数空间上。 我们的主要结果表明，$ n $ r $ r $参数张量$ \ boldsymbol {\ mathscr {m}}} \ in（0，\ infty）^{i \ times \ cdots \ cdots \ cdots \ cdots \ times i} $可以准确地估计poisson $ y ir $ ir $ ir $ ir $ ir $ ir^2（在非负典型多核分解下的非零计数。我们的结果还量化了当参数从下方统一界限时，零截断的泊松分布零截断的误差。因此，在低级多参数模型下，我们提出了一种可实施的方法，可以保证在不确定的方案中实现错误的回归，并通过虚假的零损坏。提出了几个数值实验以探索理论结果。
We propose a novel statistical inference methodology for multiway count data that is corrupted by false zeros that are indistinguishable from true zero counts. Our approach consists of zero-truncating the Poisson distribution to neglect all zero values. This simple truncated approach dispenses with the need to distinguish between true and false zero counts and reduces the amount of data to be processed. Inference is accomplished via tensor completion that imposes low-rank tensor structure on the Poisson parameter space. Our main result shows that an $N$-way rank-$R$ parametric tensor $\boldsymbol{\mathscr{M}}\in(0,\infty)^{I\times \cdots\times I}$ generating Poisson observations can be accurately estimated by zero-truncated Poisson regression from approximately $IR^2\log_2^2(I)$ non-zero counts under the nonnegative canonical polyadic decomposition. Our result also quantifies the error made by zero-truncating the Poisson distribution when the parameter is uniformly bounded from below. Therefore, under a low-rank multiparameter model, we propose an implementable approach guaranteed to achieve accurate regression in under-determined scenarios with substantial corruption by false zeros. Several numerical experiments are presented to explore the theoretical results.
