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Quantum partial least squares regression algorithm for multiple correlation problem

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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 quan-tum 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.Mean-while,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 indepen-dent 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.

quantum machine learningpartial least squares regressioneigenvalue decomposition

Yan-Yan Hou、Jian Li、Xiu-Bo Chen、Yuan Tian

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School of Artificial Intelligence,Beijing University of Post and Telecommunications,Beijing 100876,China

College of Information Science and Engineering,Zaozhuang University,Zaozhuang 277160,China

Information Security Center,State Key Laboratory of Networking and Switching Technology,Beijing University of Post and Telecommunications,Beijing 100876,China

GuiZhou University,Guizhou Provincial Key Laboratory of Public Big Data,Guiyang 550025,China

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Fundamental Research Funds for the Central Universities,ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNatu-ral Science Foundation of Beijing Municipality,ChinaTechnological Special Project of Guizhou Province,ChinaFoundation of Guizhou Provincial Key Laboratory of Public Big DataFoundation of Guizhou Provincial Key Laboratory of Public Big Data

2019XD-A02U16361066167108761170272920460014182006201830012018BDKFJJ0162018BDKFJJ018

2022

10.1088/1674-1056/ac1b84

中国物理B(英文版)
中国物理学会和中国科学院物理研究所

中国物理B(英文版)

CSTPCDCSCDSCIEI
影响因子：0.995
ISSN：1674-1056
年,卷(期)：2022.31(3)
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