Characteristic Kernels on Groups and Semigroups
K. Fukumizu, B.K. Sriperumbudur, A. Gretton and B. Schölkopf
In: The Twenty-Second Annual Conference on Neural Information Processing Systems (NIPS 2008), 8-11 Dec 2008, Vancouver, Canada.
Embeddings of random variables in reproducing kernel Hilbert spaces (RKHSs) may be used to conduct statistical inference based on higher order moments. For sufficiently rich (characteristic) RKHSs, each probability distribution has a unique embedding, allowing all statistical properties of the distribution to be taken into consideration. Necessary and sufficient conditions for an RKHS to be characteristic exist for Rn. In the present work, conditions are established for an RKHS to be characteristic on groups and semigroups. Illustrative examples are provided, including characteristic kernels on periodic domains, rotation matrices, and Rn+.