Implicit Kernel Learning

TL;DR

This paper introduces Implicit Kernel Learning (IKL), a method for learning spectral distributions of kernels using neural networks, improving performance in generative models and supervised learning tasks.

Contribution

The paper proposes a novel framework for data-driven kernel learning via implicit generative models, with simple training and sampling methods.

Findings

IKL improves performance of MMD GAN on image and text benchmarks.

IKL enhances supervised learning benchmarks over existing kernel methods.

Theoretical analysis of IKL's applicability and connections to prior methods.

Abstract

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.