Quantum-Inspired Support Vector Machine
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Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyze data for both classification and regression, whose usual complexity scales polynomially with the dimension and number of data points. Inspired by the quantum SVM, we present a quantum-inspired classical algorithm for SVM using fast sampling techniques. In our approach, we develop a general method to approximately calculate the kernel function and make classification via carefully sampling the data matrix, thus our approach can be applied to various types of SVM, such as linear SVM, poly-kernel SVM and soft SVM. Theoretical analysis shows one can find the supported hyperplanes on a data set which we have sampling access, and thus make classification with arbitrary success probability in logarithmic runtime, matching the runtime of the quantum SVM.
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