A quantum extension of SVM-perf for training nonlinear SVMs in almost linear time

Jonathan Allcock; Chang-Yu Hsieh

doi:10.22331/q-2020-10-15-342

A quantum extension of SVM-perf for training nonlinear SVMs in almost linear time

Jonathan Allcock and Chang-Yu Hsieh

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.

► BibTeX data

@article{Allcock2020quantumextensionof,
  doi = {10.22331/q-2020-10-15-342},
  url = {https://doi.org/10.22331/q-2020-10-15-342},
  title = {A quantum extension of {SVM}-perf for training nonlinear {SVM}s in almost linear time},
  author = {Allcock, Jonathan and Hsieh, Chang-Yu},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {342},
  month = oct,
  year = {2020}
}

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Cited by

[1] Iordanis Kerenidis, Anupam Prakash, and Dániel Szilágyi, "Quantum algorithms for Second-Order Cone Programming and Support Vector Machines", Quantum 5, 427 (2021).

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On SAO/NASA ADS no data on citing works was found (last attempt 2021-04-23 11:11:14).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.