Random Fourier Features for OperatorValued Kernels
Abstract
Devoted to multitask learning and structured output learning, operatorvalued kernels provide a flexible tool to build vectorvalued 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 operatorvalued kernels. We propose a general principle for Operatorvalued Random Fourier Feature construction relying on a generalization of Bochner's theorem for translationinvariant operatorvalued 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 proofofconcept shows the quality of the approximation and the efficiency of the corresponding linear models on example datasets.
 Publication:

arXiv eprints
 Pub Date:
 May 2016
 arXiv:
 arXiv:1605.02536
 Bibcode:
 2016arXiv160502536B
 Keywords:

 Computer Science  Machine Learning;
 Statistics  Machine Learning
 EPrint:
 32 pages, 6 figures