Zero-truncated Poisson regression for sparse multiway count data corrupted by false zeros

Abstract We propose a novel statistical inference methodology for multiway count data that is corrupted by false zeros are indistinguishable from true zero counts. Our approach consists of zero-truncating the Poisson distribution to neglect all values. This simple truncated dispenses with need distinguish between and counts reduces amount be processed. Inference accomplished via tensor completion imposes low-rank structure on parameter space. main result shows an $N$-way rank-$R$ parametric $\boldsymbol{\mathscr{M}}\in (0,\infty )^{I\times \cdots \times I}$ generating observations can accurately estimated zero-truncated regression approximately $IR^2\log _2^2(I)$ non-zero under nonnegative canonical polyadic decomposition. also quantifies error made when uniformly bounded below. Therefore, multiparameter model, we implementable guaranteed achieve accurate in under-determined scenarios substantial corruption zeros. Several numerical experiments presented explore theoretical results.