Robust tensor-on-tensor regression for multidimensional data modeling

In recent years, high-dimensional data, such as waveform signals and images have become ubiquitous. This type of data is often represented by multiway arrays or tensors. Several statistical models, including tensor regression, have been developed for such tensor data. However, these models are sensitive to the presence of arbitrary outliers within the tensors. To address the issue, this article proposes a Robust Tensor-On-Tensor (RTOT) regression approach, which has the capability of modeling high-dimensional data when the data is corrupted by outliers. Through several simulations and case studies, we evaluate the performance of the proposed method. The results reveal the advantage of the RTOT over some benchmarks in the literature in terms of estimation error. A Python implementation is available at https://github.com/Reisi-Lab/RTOT.git.