# Semi-parametric TEnsor Factor Analysis by Iteratively Projected Singular Value Decomposition

arXiv: https://arxiv.org/abs/2007.02404 · HTML: https://mlsanity.com/paper/2007.02404/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jul 2020.

## Built on by (most cited first, 8 of 8)

- [Online Tensor Learning: Computational and Statistical Trade-offs, Adaptivity and Optimal Regret](https://mlsanity.com/paper/2306.03372/) (2023)
- [Conditional Prediction ROC Bands for Graph Classification](https://mlsanity.com/paper/2410.15239/) (2024)
- [Conditional Uncertainty Quantification for Tensorized Topological Neural Networks](https://mlsanity.com/paper/2410.15241/) (2024)
- [Tensor-Fused Multi-View Graph Contrastive Learning](https://mlsanity.com/paper/2410.15247/) (2024)
- [Tucker Diffusion Model for High-dimensional Tensor Generation](https://mlsanity.com/paper/2604.00481/) (2026)
- [TEAFormers: TEnsor-Augmented Transformers for Multi-Dimensional Time Series Forecasting](https://mlsanity.com/paper/2410.20439/) (2024)
- [ACT-Tensor: Tensor Completion Framework for Financial Dataset Imputation](https://mlsanity.com/paper/2508.01861/) (2025)
- [Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection](https://mlsanity.com/paper/2605.19122/) (2026)

## Abstract (arXiv)

This paper introduces a general framework of Semi-parametric TEnsor Factor Analysis (STEFA) that focuses on the methodology and theory of low-rank tensor decomposition with auxiliary covariates. Semi-parametric TEnsor Factor Analysis models extend tensor factor models by incorporating auxiliary covariates in the loading matrices. We propose an algorithm of iteratively projected singular value decomposition (IP-SVD) for the semi-parametric estimation. It iteratively projects tensor data onto the linear space spanned by the basis functions of covariates and applies singular value decomposition on matricized tensors over each mode. We establish the convergence rates of the loading matrices and the core tensor factor. The theoretical results only require a sub-exponential noise distribution, which is weaker than the assumption of sub-Gaussian tail of noise in the literature. Compared with the Tucker decomposition, IP-SVD yields more accurate estimators with a faster convergence rate. Besides estimation, we propose several prediction methods with new covariates based on the STEFA model. On both synthetic and real tensor data, we demonstrate the efficacy of the STEFA model and the IP-SVD algorithm on both the estimation and prediction tasks.