Quantum-Inspired Support Vector Machine
This work addresses the big data challenge for machine learning practitioners by providing a classical algorithm with quantum-like efficiency, though it is incremental as it builds on prior quantum SVM ideas.
The authors tackled the computational scaling of least squares support vector machines (LS-SVM) by proposing a quantum-inspired classical algorithm that uses indirect sampling for kernel matrix sampling and classification, achieving logarithmic runtime in data dimension and number of points for certain data matrices, matching quantum SVM performance.
Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space and the number of data points. To tackle the big data challenge, a quantum SVM algorithm was proposed, which is claimed to achieve exponential speedup for least squares SVM (LS-SVM). Here, inspired by the quantum SVM algorithm, we present a quantum-inspired classical algorithm for LS-SVM. In our approach, a improved fast sampling technique, namely indirect sampling, is proposed for sampling the kernel matrix and classifying. We first consider the LS-SVM with a linear kernel, and then discuss the generalization of our method to non-linear kernels. Theoretical analysis shows our algorithm can make classification with arbitrary success probability in logarithmic runtime of both the dimension of data space and the number of data points for low rank, low condition number and high dimensional data matrix, matching the runtime of the quantum SVM.