# CP Factor Model for Dynamic Tensors

arXiv: https://arxiv.org/abs/2110.15517 · HTML: https://mlsanity.com/paper/2110.15517/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2021.

## Built on by (most cited first, 10 of 10)

- [Factor Augmented Tensor-on-Tensor Neural Networks](https://mlsanity.com/paper/2405.19610/) (2024)
- [Modelling matrix time series via a tensor CP-decomposition](https://mlsanity.com/paper/2112.15423/) (2021)
- [Covariate-Adjusted Deep Causal Learning for Heterogeneous Panel Data Models](https://mlsanity.com/paper/2505.20536/) (2025)
- [Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA](https://mlsanity.com/paper/2202.04719/) (2022)
- [Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges](https://mlsanity.com/paper/2405.18412/) (2024)
- [TEAFormers: TEnsor-Augmented Transformers for Multi-Dimensional Time Series Forecasting](https://mlsanity.com/paper/2410.20439/) (2024)
- [Supervised Dynamic Dimension Reduction with Deep Neural Network](https://mlsanity.com/paper/2508.03546/) (2025)
- [ACT-Tensor: Tensor Completion Framework for Financial Dataset Imputation](https://mlsanity.com/paper/2508.01861/) (2025)
- [Are Whitepaper Claims Reflected in Market Structure? A Contamination-Aware Pipeline and a Power-Limited Null](https://mlsanity.com/paper/2601.20336/) (2026)
- [Factor Augmented High-Dimensional SGD](https://mlsanity.com/paper/2605.19291/) (2026)

## Abstract (arXiv)

Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CP decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tensor factor models based on Tucker-type tensor decomposition. The model structure allows for a set of uncorrelated one-dimensional latent dynamic factor processes, making it much more convenient to study the underlying dynamics of the time series. A new high order projection estimator is proposed for such a factor model, utilizing the special structure and the idea of the higher order orthogonal iteration procedures commonly used in Tucker-type tensor factor model and general tensor CP decomposition procedures. Theoretical investigation provides statistical error bounds for the proposed methods, which shows the significant advantage of utilizing the special model structure. Simulation study is conducted to further demonstrate the finite sample properties of the estimators. Real data application is used to illustrate the model and its interpretations.