Quantum partial least squares regression algorithm for multiple correlation problem  

作　　者：Yan-Yan Hou Jian Li Xiu-Bo Chen Yuan Tian 侯艳艳;李剑;陈秀波;田源(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)

机构地区：[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

出　　处：《Chinese Physics B》2022年第3期177-186,共10页中国物理B（英文版）

基　　金：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);the Foundation of Guizhou Provincial Key Laboratory of Public Big Data (Grant Nos. 2018BDKFJJ016 and 2018BDKFJJ018)。

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 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]