  Kernels are powerful and versatile tools in machine learning and statistics.
Although the notion of universal kernels and characteristic kernels has been
studied, kernel selection still greatly influences the empirical performance.
While learning the kernel in a data driven way has been investigated, in this
paper we explore learning the spectral distribution of kernel via implicit
generative models parametrized by deep neural networks. We called our method
Implicit Kernel Learning (IKL). The proposed framework is simple to train and
inference is performed via sampling random Fourier features. We investigate two
applications of the proposed IKL as examples, including generative adversarial
networks with MMD (MMD GAN) and standard supervised learning. Empirically, MMD
GAN with IKL outperforms vanilla predefined kernels on both image and text
generation benchmarks; using IKL with Random Kitchen Sinks also leads to
substantial improvement over existing state-of-the-art kernel learning
algorithms on popular supervised learning benchmarks. Theory and conditions for
using IKL in both applications are also studied as well as connections to
previous state-of-the-art methods.
