Tensor on Tensor Regression

Tensor-on-tensor (ToT) regression focuses on predicting tensor-valued outputs from tensor-valued inputs, extending traditional regression to higher-dimensional data structures. Current research emphasizes efficient algorithms, such as those based on tensor train decompositions and Riemannian optimization, to address the computational challenges posed by the exponential growth in tensor complexity. These advancements are improving prediction accuracy and computational efficiency in various applications, including human motion prediction and image analysis, by leveraging the inherent structure within tensor data. The development of robust and scalable ToT regression models is significantly impacting fields requiring the analysis of complex, multi-dimensional data.