Quantum partial least squares regression algorithm for multiple correlation problem |
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| Affiliation: | 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 |
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| 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. |
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| Keywords: | quantum machine learning partial least squares regression eigenvalue decomposition |
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