# Distributed Flexible Nonlinear Tensor Factorization

arXiv: https://arxiv.org/abs/1604.07928 · HTML: https://mlsanity.com/paper/1604.07928/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2016.

## Built on by (most cited first, 15 of 15)

- [Nonparametric Factor Trajectory Learning for Dynamic Tensor Decomposition](https://mlsanity.com/paper/2207.02446/) (2022)
- [Nonparametric Sparse Tensor Factorization with Hierarchical Gamma Processes](https://mlsanity.com/paper/2110.10082/) (2021)
- [Streaming Factor Trajectory Learning for Temporal Tensor Decomposition](https://mlsanity.com/paper/2310.17021/) (2023)
- [Nonparametric Embeddings of Sparse High-Order Interaction Events](https://mlsanity.com/paper/2207.03639/) (2022)
- [SiBBlInGS: Similarity-driven Building-Block Inference using Graphs across States](https://mlsanity.com/paper/2306.04817/) (2023)
- [Dynamic Tensor Decomposition via Neural Diffusion-Reaction Processes](https://mlsanity.com/paper/2310.19666/) (2023)
- [Cherry-Picking Gradients: Learning Low-Rank Embeddings of Visual Data via Differentiable Cross-Approximation](https://mlsanity.com/paper/2105.14250/) (2021)
- [Efficient Nonparametric Tensor Decomposition for Binary and Count Data](https://mlsanity.com/paper/2401.07711/) (2024)
- [Functional Complexity-adaptive Temporal Tensor Decomposition](https://mlsanity.com/paper/2502.06164/) (2025)
- [Multi-Integration of Labels across Categories for Component Identification (MILCCI)](https://mlsanity.com/paper/2602.04270/) (2026)
- [MLCTR: A Fast Scalable Coupled Tensor Completion Based on Multi-Layer Non-Linear Matrix Factorization](https://mlsanity.com/paper/2109.01773/) (2021)
- [Streaming data recovery via Bayesian tensor train decomposition](https://mlsanity.com/paper/2302.12148/) (2023)
- [HeTriNet: Heterogeneous Graph Triplet Attention Network for Drug-Target-Disease Interaction](https://mlsanity.com/paper/2312.00189/) (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)

Tensor factorization is a powerful tool to analyse multi-way data. Compared with traditional multi-linear methods, nonlinear tensor factorization models are capable of capturing more complex relationships in the data. However, they are computationally expensive and may suffer severe learning bias in case of extreme data sparsity. To overcome these limitations, in this paper we propose a distributed, flexible nonlinear tensor factorization model. Our model can effectively avoid the expensive computations and structural restrictions of the Kronecker-product in existing TGP formulations, allowing an arbitrary subset of tensorial entries to be selected to contribute to the training. At the same time, we derive a tractable and tight variational evidence lower bound (ELBO) that enables highly decoupled, parallel computations and high-quality inference. Based on the new bound, we develop a distributed inference algorithm in the MapReduce framework, which is key-value-free and can fully exploit the memory cache mechanism in fast MapReduce systems such as SPARK. Experimental results fully demonstrate the advantages of our method over several state-of-the-art approaches, in terms of both predictive performance and computational efficiency. Moreover, our approach shows a promising potential in the application of Click-Through-Rate (CTR) prediction for online advertising.