Random Fourier Features For Operator-Valued Kernels

Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the celebrated Random Fourier Feature methodology to get an approximation of operator-valued kernels. We propose a general principle for Operator-valued Random Fourier Feature construction relying on a generalization of Bochner’s theorem for translation-invariant operator-valued Mercer kernels. We prove the uniform convergence of the kernel approximation for bounded and unbounded operator random Fourier features using appropriate Bernstein matrix concentration inequality. An experimental proof-of-concept shows the quality of the approximation and the efficiency of the corresponding linear models on example datasets.

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Brault, R, Heinonen, M & d'Alché-Buc, F 2016, Random Fourier Features For Operator-Valued Kernels. in B Durrant & K-E Kim (eds), Proceedings of the 8th Asian Conference on Machine Learning. Proceedings of Machine Learning Research, vol. 63, JMLR, pp. 110-125, Asian Conference on Machine Learning, Hamilton, New Zealand, 16/11/2016. < http://proceedings.mlr.press/v63/Brault39.html >

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https://urn.fi/URN:NBN:fi:aalto-201710157164

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[article-cris] Perustieteiden korkeakoulu / SCI

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