# Streaming Factor Trajectory Learning for Temporal Tensor Decomposition

arXiv: https://arxiv.org/abs/2310.17021 · HTML: https://mlsanity.com/paper/2310.17021/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 25 Oct 2023.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Streaming Variational Bayes](https://mlsanity.com/paper/1307.6769/) (2013)
- [Tractable Inference for Complex Stochastic Processes](https://mlsanity.com/paper/1301.7362/) (2013)
- [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)
- [Dynamic Tensor Recommender Systems](https://mlsanity.com/paper/2003.05568/) (2020)
- [Bayesian Conditional Tensor Factorizations for High-Dimensional Classification](https://mlsanity.com/paper/1301.4950/) (2013)
- [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)
- [Conditional Expectation Propagation](https://mlsanity.com/paper/1910.12360/) (2019)
- [Bounding errors of Expectation-Propagation](https://mlsanity.com/paper/1601.02387/) (2016)

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

- [Functional Bayesian Tucker Decomposition for Continuous-indexed Tensor Data](https://mlsanity.com/paper/2311.04829/) (2023)
- [Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observations](https://mlsanity.com/paper/2505.09284/) (2025)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Functional Complexity-adaptive Temporal Tensor Decomposition](https://mlsanity.com/paper/2502.06164/) (2025)
- [StreamPhy: Streaming Inference of High-Dimensional Physical Dynamics via State Space Models](https://mlsanity.com/paper/2605.07384/) (2026)
- [TRACE: Retrospective Streaming Generation of Physical Fields under Sparse Structured Sensing](https://mlsanity.com/paper/2608.26219/) (2026)

## Abstract (arXiv)

Practical tensor data is often along with time information. Most existing temporal decomposition approaches estimate a set of fixed factors for the objects in each tensor mode, and hence cannot capture the temporal evolution of the objects' representation. More important, we lack an effective approach to capture such evolution from streaming data, which is common in real-world applications. To address these issues, we propose Streaming Factor Trajectory Learning for temporal tensor decomposition. We use Gaussian processes (GPs) to model the trajectory of factors so as to flexibly estimate their temporal evolution. To address the computational challenges in handling streaming data, we convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE). We develop an efficient online filtering algorithm to estimate a decoupled running posterior of the involved factor states upon receiving new data. The decoupled estimation enables us to conduct standard Rauch-Tung-Striebel smoothing to compute the full posterior of all the trajectories in parallel, without the need for revisiting any previous data. We have shown the advantage of SFTL in both synthetic tasks and real-world applications. The code is available at {https://github.com/xuangu-fang/Streaming-Factor-Trajectory-Learning}.