Random Fourier Features for Operator-Valued Kernels
This work addresses scalability issues for researchers and practitioners in multi-task learning, but it is incremental as it adapts an existing method to a specific kernel type.
The authors tackled the scalability of operator-valued kernel methods in multi-task and structured output learning by extending Random Fourier Features to approximate these kernels, achieving efficient linear models with experimental validation.
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.