受假零污染的多路稀疏计数数据的零截断泊松回归
Zero-Truncated Poisson Regression for Sparse Multiway Count Data Corrupted by False Zeros
AI总结：
针对受假零污染的多路稀疏计数数据，提出零截断泊松回归方法，通过张量补全估计低秩泊松参数，理论保证在欠定场景下实现准确回归。
摘要：
我们提出了一种新颖的统计推断方法，用于处理被假零污染的多路计数数据，这些假零与真实零计数无法区分。我们的方法包括对泊松分布进行零截断，以忽略所有零值。这种简单的截断方法无需区分真实零计数和假零计数，并减少了需要处理的数据量。推断通过张量补全完成，该补全在泊松参数空间上施加低秩张量结构。我们的主要结果表明，在非负典型多元分解下，一个生成泊松观测的$N$路秩为$R$的参数张量$\boldsymbol{\mathscr{M}}\in(0,\infty)^{I\times \cdots\times I}$可以通过零截断泊松回归从大约$IR^2\log_2^2(I)$个非零计数中准确估计。我们的结果还量化了当参数一致有下界时，对泊松分布进行零截断所产生的误差。因此，在低秩多参数模型下，我们提出了一种可实现的方法，保证在欠定场景且存在大量假零污染的情况下实现准确回归。我们进行了若干数值实验来探索理论结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
