# Nonparametric Sparse Tensor Factorization with Hierarchical Gamma Processes

arXiv: https://arxiv.org/abs/2110.10082 · HTML: https://mlsanity.com/paper/2110.10082/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 65 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Builds on (most cited first, 10 of 10)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations](https://mlsanity.com/paper/1606.01855/) (2016)
- [Sparse graphs using exchangeable random measures](https://mlsanity.com/paper/1401.1137/) (2014)
- [Bayesian Poisson Tensor Factorization for Inferring Multilateral Relations from Sparse Dyadic Event Counts](https://mlsanity.com/paper/1506.03493/) (2015)
- [Distributed Flexible Nonlinear Tensor Factorization](https://mlsanity.com/paper/1604.07928/) (2016)
- [Scalable Tucker Factorization for Sparse Tensors - Algorithms and Discoveries](https://mlsanity.com/paper/1710.02261/) (2017)
- [DFacTo: Distributed Factorization of Tensors](https://mlsanity.com/paper/1406.4519/) (2014)
- [Bayesian Conditional Tensor Factorizations for High-Dimensional Classification](https://mlsanity.com/paper/1301.4950/) (2013)
- [Zero-Truncated Poisson Tensor Factorization for Massive Binary Tensors](https://mlsanity.com/paper/1508.04210/) (2015)

## Built on by (most cited first, 6 of 6)

- [Nonparametric Factor Trajectory Learning for Dynamic Tensor Decomposition](https://mlsanity.com/paper/2207.02446/) (2022)
- [Streaming Factor Trajectory Learning for Temporal Tensor Decomposition](https://mlsanity.com/paper/2310.17021/) (2023)
- [Dynamic Tensor Decomposition via Neural Diffusion-Reaction Processes](https://mlsanity.com/paper/2310.19666/) (2023)
- [Graphical Dirichlet Process for Clustering Non-Exchangeable Grouped Data](https://mlsanity.com/paper/2302.09111/) (2023)
- [Score-Based Model for Low-Rank Tensor Recovery](https://mlsanity.com/paper/2506.22295/) (2025)
- [Bayesian Tensor Decomposition with Diffusion Model Prior](https://mlsanity.com/paper/2606.03212/) (2026)

## Abstract (arXiv)

We propose a nonparametric factorization approach for sparsely observed tensors. The sparsity does not mean zero-valued entries are massive or dominated. Rather, it implies the observed entries are very few, and even fewer with the growth of the tensor; this is ubiquitous in practice. Compared with the existent works, our model not only leverages the structural information underlying the observed entry indices, but also provides extra interpretability and flexibility -- it can simultaneously estimate a set of location factors about the intrinsic properties of the tensor nodes, and another set of sociability factors reflecting their extrovert activity in interacting with others; users are free to choose a trade-off between the two types of factors. Specifically, we use hierarchical Gamma processes and Poisson random measures to construct a tensor-valued process, which can freely sample the two types of factors to generate tensors and always guarantees an asymptotic sparsity. We then normalize the tensor process to obtain hierarchical Dirichlet processes to sample each observed entry index, and use a Gaussian process to sample the entry value as a nonlinear function of the factors, so as to capture both the sparse structure properties and complex node relationships. For efficient inference, we use Dirichlet process properties over finite sample partitions, density transformations, and random features to develop a stochastic variational estimation algorithm. We demonstrate the advantage of our method in several benchmark datasets.