This paper proposes the Robust Modewise Factor Model (RMFM) to address missing data and outliers in tensor-valued time series. The framework employs mode-specific generalized M-estimators to handle heterogeneous noise characteristics across different tensor modes, integrated with a scalable block coordinate descent algorithm. Theoretical analysis establishes consistency and asymptotic normality under general missing patterns and weak factor presence. Experiments on traffic, electricity, and macroeconomic datasets demonstrate up to 35% reduction in imputation error and robustness to 20% outlier contamination compared to state-of-the-art methods.
Key findings
RMFM simultaneously handles missing data, outliers, and multiway dependencies in tensor time series through a unified framework.
Mode-specific robust estimation adapts to heterogeneous noise patterns, such as sparse spatial outliers versus dense temporal noise.
Theoretical guarantees establish consistency and asymptotic normality under MCAR/MAR missing mechanisms and weak factor presence.
Block coordinate descent algorithm achieves linear scalability and O(1/k) convergence rate with closed-form updates.
Empirical validation shows 35% lower imputation error and robustness to 20% contamination on real-world traffic, electricity, and macroeconomic benchmarks.
Limitations & open questions
Theoretical guarantees assume specific missing data mechanisms (MCAR/MAR) which may not hold in all real-world scenarios.
Performance and scalability under extreme outlier contamination rates significantly exceeding 20% are not fully explored.
Methodological complexity may limit adoption without specialized expertise in tensor decomposition and robust statistics.