中国物理B ›› 2022, Vol. 31 ›› Issue (3): 30304-030304.doi: 10.1088/1674-1056/ac1b84

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Quantum partial least squares regression algorithm for multiple correlation problem

Yan-Yan Hou(侯艳艳)1,2,3, Jian Li(李剑)1,†, Xiu-Bo Chen(陈秀波)3,4, and Yuan Tian(田源)1   

  1. 1 School of Artificial Intelligence, Beijing University of Post and Telecommunications, Beijing 100876, China;
    2 College of Information Science and Engineering, Zaozhuang University, Zaozhuang 277160, China;
    3 Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Post and Telecommunications, Beijing 100876, China;
    4 GuiZhou University, Guizhou Provincial Key Laboratory of Public Big Data, Guiyang 550025, China
  • 收稿日期:2021-04-27 修回日期:2021-08-04 接受日期:2021-08-07 出版日期:2022-02-22 发布日期:2022-02-17
  • 通讯作者: Jian Li E-mail:lijian@bupt.edu.cn
  • 基金资助:
    Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2019XD-A02), the National Natural Science Foundation of China (Grant Nos. U1636106, 61671087, 61170272, and 92046001), Natural Science Foundation of Beijing Municipality, China (Grant No. 4182006), Technological Special Project of Guizhou Province, China (Grant No. 20183001), and the Foundation of Guizhou Provincial Key Laboratory of Public Big Data (Grant Nos. 2018BDKFJJ016 and 2018BDKFJJ018).

Quantum partial least squares regression algorithm for multiple correlation problem

Yan-Yan Hou(侯艳艳)1,2,3, Jian Li(李剑)1,†, Xiu-Bo Chen(陈秀波)3,4, and Yuan Tian(田源)1   

  1. 1 School of Artificial Intelligence, Beijing University of Post and Telecommunications, Beijing 100876, China;
    2 College of Information Science and Engineering, Zaozhuang University, Zaozhuang 277160, China;
    3 Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Post and Telecommunications, Beijing 100876, China;
    4 GuiZhou University, Guizhou Provincial Key Laboratory of Public Big Data, Guiyang 550025, China
  • Received:2021-04-27 Revised:2021-08-04 Accepted:2021-08-07 Online:2022-02-22 Published:2022-02-17
  • Contact: Jian Li E-mail:lijian@bupt.edu.cn
  • Supported by:
    Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2019XD-A02), the National Natural Science Foundation of China (Grant Nos. U1636106, 61671087, 61170272, and 92046001), Natural Science Foundation of Beijing Municipality, China (Grant No. 4182006), Technological Special Project of Guizhou Province, China (Grant No. 20183001), and the Foundation of Guizhou Provincial Key Laboratory of Public Big Data (Grant Nos. 2018BDKFJJ016 and 2018BDKFJJ018).

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摘要： Partial least squares (PLS) regression is an important linear regression method that efficiently addresses the multiple correlation problem by combining principal component analysis and multiple regression. In this paper, we present a quantum partial least squares (QPLS) regression algorithm. To solve the high time complexity of the PLS regression, we design a quantum eigenvector search method to speed up principal components and regression parameters construction. Meanwhile, we give a density matrix product method to avoid multiple access to quantum random access memory (QRAM) during building residual matrices. The time and space complexities of the QPLS regression are logarithmic in the independent variable dimension n, the dependent variable dimension w, and the number of variables m. This algorithm achieves exponential speed-ups over the PLS regression on n, m, and w. In addition, the QPLS regression inspires us to explore more potential quantum machine learning applications in future works.

关键词: quantum machine learning, partial least squares regression, eigenvalue decomposition

Abstract: Partial least squares (PLS) regression is an important linear regression method that efficiently addresses the multiple correlation problem by combining principal component analysis and multiple regression. In this paper, we present a quantum partial least squares (QPLS) regression algorithm. To solve the high time complexity of the PLS regression, we design a quantum eigenvector search method to speed up principal components and regression parameters construction. Meanwhile, we give a density matrix product method to avoid multiple access to quantum random access memory (QRAM) during building residual matrices. The time and space complexities of the QPLS regression are logarithmic in the independent variable dimension n, the dependent variable dimension w, and the number of variables m. This algorithm achieves exponential speed-ups over the PLS regression on n, m, and w. In addition, the QPLS regression inspires us to explore more potential quantum machine learning applications in future works.

Key words: quantum machine learning, partial least squares regression, eigenvalue decomposition

中图分类号:  (Quantum algorithms, protocols, and simulations)

  • 03.67.Ac
03.67.Lx (Quantum computation architectures and implementations)