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Annual Review of Statistics and Its Application

Volume 12, 2025

Tensors in High-Dimensional Data Analysis: Methodological Opportunities and Theoretical Challenges

  • Arnab Auddy1, Dong Xia2 and Ming Yuan3
  • 1Department of Statistics, The Ohio State University, Columbus, Ohio, USA 2Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China 3Department of Statistics, Columbia University, New York, NY, USA; email: [email protected]
  • Vol. 12:527-551 (Volume publication date March 2025)
  • First published as a Review in Advance on November 12, 2024
  • Copyright © 2025 by the author(s).
    This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. See credit lines of images or other third-party material in this article for license information.

Abstract

Large amounts of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity of such data provides vast new opportunities for modeling and analysis, but efficiently extracting information content from them, both statistically and computationally, presents unique and fundamental challenges. Addressing these challenges requires an interdisciplinary approach that brings together tools and insights from statistics, optimization, and numerical linear algebra, among other fields. Despite these hurdles, significant progress has been made in the past decade. This review seeks to examine some of the key advancements and identify common threads among them, under a number of different statistical settings.

Keyword(s): computational efficiency, high-dimensional data analysis, statistical optimality, tensors
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2025-03-07
2025-06-20
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Tensors in High-Dimensional Data Analysis: Methodological Opportunities and Theoretical Challenges
Annual Review of Statistics and Its Application 12, 527 (2025); https://doi.org/10.1146/annurev-statistics-112723-034548
/content/journals/10.1146/annurev-statistics-112723-034548
/content/journals/10.1146/annurev-statistics-112723-034548
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