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 operatorvalued kernels. We propose a general principle for Operator-valued Random Fourier ∗[email protected] †[email protected] ‡[email protected] 1 ar X iv :1 60 5. 02 53 6v 2 [ cs .L G ] 2 3 M ay 2 01 6 Feature construction relying on a generalization of Bochner’s theorem for translationinvariant 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.