2017/08/01 by Masaaki Imaizumi, Imaizumi, Masaaki, Takanori Maehara +3
Engineering · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1708.00132
openalex publication_date 2017/08/01 · openalex created_date 2017/08/17 · openalex updated_date 2026/07/28
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of statistical theory and of scalable algorithms. In this paper, we address the limitations. First, we introduce a convex relaxation of the TT decomposition problem and derive its error bound for the tensor completion task. Next, we develop an alternating optimization method with a randomization technique, in which the time complexity is as efficient as the space complexity is. In experiments, we numerically confirm the derived bounds and empirically demonstrate the performance of our method with a real higher-order tensor.