Research Paper#Time Series Analysis, Matrix Factorization, Machine Learning🔬 ResearchAnalyzed: Jan 3, 2026 06:13
Modewise Additive Factor Model for Matrix Time Series
Published:Dec 31, 2025 18:24
•1 min read
•ArXiv
Analysis
This paper introduces a novel Modewise Additive Factor Model (MAFM) for matrix-valued time series, offering a more flexible approach than existing multiplicative factor models like Tucker and CP. The key innovation lies in its additive structure, allowing for separate modeling of row-specific and column-specific latent effects. The paper's contribution is significant because it provides a computationally efficient estimation procedure (MINE and COMPAS) and a data-driven inference framework, including convergence rates, asymptotic distributions, and consistent covariance estimators. The development of matrix Bernstein inequalities for quadratic forms of dependent matrix time series is a valuable technical contribution. The paper's focus on matrix time series analysis is relevant to various fields, including finance, signal processing, and recommendation systems.
Key Takeaways
- •Introduces MAFM, a novel additive factor model for matrix-valued time series.
- •Offers greater flexibility than multiplicative factor models.
- •Develops a computationally efficient two-stage estimation procedure (MINE and COMPAS).
- •Provides a data-driven inference framework with convergence rates and asymptotic distributions.
- •Includes a technical contribution: matrix Bernstein inequalities for quadratic forms of dependent matrix time series.
Reference
“The key methodological innovation is that orthogonal complement projections completely eliminate cross-modal interference when estimating each loading space.”