Random Fourier Features For Operator-Valued Kernels
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Proceedings of the 8th Asian Conference on Machine Learning, Proceedings of Machine Learning Research, Volume 63
AbstractDevoted 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.
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 >