Robust Gradient Optimization for Dynamic High-Dimensional Tensor Data via Tucker Decomposition

We propose a robust Tucker-based tensor factor model for high-dimensional tensor time series, designed to mitigate the impact of outliers and irregular noise. Replacing the squared loss with the parameter-free log-cosh loss, we develop an efficient element-wise iterative optimization scheme for estimating the loading matrices and factor tensors. Under mild regularity conditions that allow outlier-prone idiosyncratic errors, we establish theoretical guarantees for the proposed estimator, including convergence rates and finite-sample error bounds for signal reconstruction and parameter estimation. Extensive simulations across a range of distributional settings demonstrate that the proposed approach consistently improves accuracy and robustness over existing methods, particularly in high-dimensional and noisy regimes. Applications to multimodal video tensors and high-dimensional financial portfolios further validate its practical utility, yielding clearer motion recovery, more interpretable loading patterns, and pronounced seasonal factor effects.