A quantum extension of SVM-perf for training nonlinear SVMs in almost linear time
This work addresses the efficiency bottleneck in training nonlinear SVMs for machine learning applications, offering a quantum speedup over classical methods, though it is incremental as it builds on existing algorithms.
The authors tackled the problem of training nonlinear support vector machines (SVMs) efficiently by proposing a quantum algorithm based on SVM-perf, achieving a running time that scales linearly with the number of training examples for the standard soft-margin model, with classical simulations showing practical performance.
We propose a quantum algorithm for training nonlinear support vector machines (SVM) for feature space learning where classical input data is encoded in the amplitudes of quantum states. Based on the classical SVM-perf algorithm of Joachims, our algorithm has a running time which scales linearly in the number of training examples $m$ (up to polylogarithmic factors) and applies to the standard soft-margin $\ell_1$-SVM model. In contrast, while classical SVM-perf has demonstrated impressive performance on both linear and nonlinear SVMs, its efficiency is guaranteed only in certain cases: it achieves linear $m$ scaling only for linear SVMs, where classification is performed in the original input data space, or for the special cases of low-rank or shift-invariant kernels. Similarly, previously proposed quantum algorithms either have super-linear scaling in $m$, or else apply to different SVM models such as the hard-margin or least squares $\ell_2$-SVM which lack certain desirable properties of the soft-margin $\ell_1$-SVM model. We classically simulate our algorithm and give evidence that it can perform well in practice, and not only for asymptotically large data sets.