抄録
Offer Organization: Japan Society for the Promotion of Science, System Name: Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B), Category: Grant-in-Aid for Young Scientists (B), Fund Type: competitive_research_funding, Overall Grant Amount: - (direct: 2000000, indirect: 600000)
Kernel Bayes Inference (KBI), which is a Bayesian inference based on kernel methods, has been studied. KBI infers kernel means, which are features of probability distributions in reproducing kernel Hilbert space. In KBI, characteristic kernels play an important role in specifying probability distributions by kernel means. We studied a connection between characteristic kernels and infinitely divisible distributions. We showed that continuous bounded and symmetric density functions of infinitely divisible distributions can be used for characteristic kernels. Within the infinitely divisible distributions, we proposed a convolution trick, which is a generalization of the kernel trick. The convolution trick can be used for developing various kernel algorithms that combine infinitely divisible distributions.