Implicit Kernel Learning
This work addresses kernel selection for machine learning practitioners, offering a data-driven approach that is incremental but shows strong empirical gains.
The paper tackles the problem of kernel selection in machine learning by proposing Implicit Kernel Learning (IKL), a method that learns the spectral distribution of kernels using implicit generative models with deep neural networks, resulting in improved performance over predefined kernels in generative adversarial networks and supervised learning benchmarks.
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.