A quantum extension of SVM-perf for training nonlinear SVMs in almost linear time
Tencent Quantum Laboratory
| Published: | 2020-10-15, volume 4, page 342 |
| Eprint: | arXiv:2006.10299v3 |
| Doi: | https://doi.org/10.22331/q-2020-10-15-342 |
| Citation: | Quantum 4, 342 (2020). |
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Abstract
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 [1], 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.
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► References
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