A Hilbert space embedding of a distribution---in short, a kernel mean
embedding---has recently emerged as a powerful tool for machine learning and
inference. The basic idea behind this framework is to map distributions into a
reproducing kernel Hilbert space (RKHS) in which the whole arsenal of kernel
methods can be extended to probability measures. It can be viewed as a
generalization of the original "feature map" common to support vector machines
(SVMs) and other kernel methods. While initially closely associated with the
latter, it has meanwhile found application in fields ranging from kernel
machines and probabilistic modeling to statistical inference, causal discovery,
and deep learning. The goal of this survey is to give a comprehensive review of
existing work and recent advances in this research area, and to discuss the
most challenging issues and open problems that could lead to new research
directions. The survey begins with a brief introduction to the RKHS and
positive definite kernels which forms the backbone of this survey, followed by
a thorough discussion of the Hilbert space embedding of marginal distributions,
theoretical guarantees, and a review of its applications. The embedding of
distributions enables us to apply RKHS methods to probability measures which
prompts a wide range of applications such as kernel two-sample testing,
independent testing, and learning on distributional data. Next, we discuss the
Hilbert space embedding for conditional distributions, give theoretical
insights, and review some applications. The conditional mean embedding enables
us to perform sum, product, and Bayes' rules---which are ubiquitous in
graphical model, probabilistic inference, and reinforcement learning---in a
non-parametric way. We then discuss relationships between this framework and
other related areas. Lastly, we give some suggestions on future research
directions.

该文介绍了一种基于希尔伯特空间嵌入的分布表征方法，该方法利用再生核希尔伯特空间将分布映射到一个空间中，并扩展了一般支持向量机和其他核方法的整个内核方法库，为概率测量、统计推断、因果发现和深度学习等领域提供了广泛应用，并讨论了该方法的理论保证，应用和未来的研究方向。