Structured Tensor Approximation under Kronecker Graph and Its Application on Hydrological Data

2021 Fiscal Year Final Research Report

• Project/Area Number: 20K19875
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 61030:Intelligent informatics-related
• Research Institution: Institute of Physical and Chemical Research
• Principal Investigator: Li Chao 国立研究開発法人理化学研究所, 革新知能統合研究センター, 研究員 (10869837)
• Project Period (FY): 2020-04-01 – 2022-03-31
• Keywords: tensor network

Outline of Final Research Achievements

Tensor models have been widely applied to resolving extremely high-dimensional tasks in various fields. However, there remain many unexplored problems for tensors, particularly for tensor network structure search (TN-SS) and the analysis of the tensor learning dynamics (TLD). In this project, we conduct a thorough investigation of the preceding issues. For TN-SS, we found that the optimal tensor network structure can be obtained by sampling-based algorithms, for which we propose two efficient sampling schemes with theoretical analysis of the search space. For analyzing TLD in time series forecasting, our study reveals the relationship between the models’ memory mechanism and the tensor orders. We also propose a new forecasting method called the fractional tensor recurrent unit (fTRU), which can maximize the benefit of the long-memory effect by tensors. Extensive experimental results on real-world data demonstrate the usefulness of the methods studied in the project.

Free Research Field

machine learning

Academic Significance and Societal Importance of the Research Achievements

Tensor is a promising framework, which tightly bonds many scientific fields for the human society. The results of the project reveal how the tensor structures impact its behavior in machine learning and practically provides methods to maximize the performance in real-world applications.