# Zero-Truncated Poisson Regression for Sparse Multiway Count Data Corrupted by False Zeros

arXiv: https://arxiv.org/abs/2201.10014 · HTML: https://mlsanity.com/paper/2201.10014/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 56 references that are in the map.
- First posted on arXiv 25 Jan 2022.

## Builds on (most cited first, 18 of 18)

- [Text Classification Algorithms: A Survey](https://mlsanity.com/paper/1904.08067/) (2019)
- [Top2Vec: Distributed Representations of Topics](https://mlsanity.com/paper/2008.09470/) (2020)
- [Nonconvex Low-Rank Tensor Completion from Noisy Data](https://mlsanity.com/paper/1911.04436/) (2019)
- [Generalized Canonical Polyadic Tensor Decomposition](https://mlsanity.com/paper/1808.07452/) (2018)
- [On Tensor Completion via Nuclear Norm Minimization](https://mlsanity.com/paper/1405.1773/) (2014)
- [Provable Tensor Factorization with Missing Data](https://mlsanity.com/paper/1406.2784/) (2014)
- [Spectral algorithms for tensor completion](https://mlsanity.com/paper/1612.07866/) (2016)
- [Infinite Edge Partition Models for Overlapping Community Detection and Link Prediction](https://mlsanity.com/paper/1501.06218/) (2015)
- [Low-Rank Matrix and Tensor Completion via Adaptive Sampling](https://mlsanity.com/paper/1304.4672/) (2013)
- [Stochastic Gradients for Large-Scale Tensor Decomposition](https://mlsanity.com/paper/1906.01687/) (2019)
- [Real-time 3D reconstruction from single-photon lidar data using plug-and-play point cloud denoisers](https://mlsanity.com/paper/1905.06700/) (2019)
- [Learning tensors from partial binary measurements](https://mlsanity.com/paper/1804.00108/) (2018)
- [Variational inference for sparse network reconstruction from count data](https://mlsanity.com/paper/1806.03120/) (2018)
- [Incoherent Tensor Norms and Their Applications in Higher Order Tensor Completion](https://mlsanity.com/paper/1606.03504/) (2016)
- [Poisson Matrix Recovery and Completion](https://mlsanity.com/paper/1504.05229/) (2015)
- [Near-optimal sample complexity for convex tensor completion](https://mlsanity.com/paper/1711.04965/) (2017)
- [Nonnegative Tensor Completion via Integer Optimization](https://mlsanity.com/paper/2111.04580/) (2021)
- [Zero-Truncated Poisson Tensor Factorization for Massive Binary Tensors](https://mlsanity.com/paper/1508.04210/) (2015)

## Built on by (most cited first, 3 of 3)

- [Spectral gap-based deterministic tensor completion](https://mlsanity.com/paper/2306.06262/) (2023)
- [Near-Efficient and Non-Asymptotic Multiway Inference](https://mlsanity.com/paper/2511.05368/) (2025)
- [Nonnegative Matrix Factorization in the Component-Wise L1 Norm for Sparse Data](https://mlsanity.com/paper/2603.29715/) (2026)

## Abstract (arXiv)

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 boldsymbolmathscrM∈(0,∞)I× cdots× I generating Poisson observations can be accurately estimated by zero-truncated Poisson regression from approximately IR2log22(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.