# Zero-Truncated Poisson Tensor Factorization for Massive Binary Tensors

arXiv: https://arxiv.org/abs/1508.04210 · HTML: https://mlsanity.com/paper/1508.04210/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2015.

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

- [Nonparametric Sparse Tensor Factorization with Hierarchical Gamma Processes](https://mlsanity.com/paper/2110.10082/) (2021)
- [Nonparametric Embeddings of Sparse High-Order Interaction Events](https://mlsanity.com/paper/2207.03639/) (2022)
- [Zero-Truncated Poisson Regression for Sparse Multiway Count Data Corrupted by False Zeros](https://mlsanity.com/paper/2201.10014/) (2022)

## Abstract (arXiv)

We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood, using a zero-truncated Poisson likelihood for binary data allows our model to scale up in the number of ones in the tensor, which is especially appealing for massive but sparse binary tensors; (2) side-information in form of binary pairwise relationships (e.g., an adjacency network) between objects in any tensor mode can also be leveraged, which can be especially useful in "cold-start" settings; and (3) the model admits simple Bayesian inference via batch, as well as online MCMC; the latter allows scaling up even for dense binary data (i.e., when the number of ones in the tensor/network is also massive). In addition, non-negative factor matrices in our model provide easy interpretability, and the tensor rank can be inferred from the data. We evaluate our model on several large-scale real-world binary tensors, achieving excellent computational scalability, and also demonstrate its usefulness in leveraging side-information provided in form of mode-network(s).