Kernel Bayes Inference and Infinitely Divisible Distributions

2016 Fiscal Year Final Research Report

• Project/Area Number: 26870821
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Intelligent informatics; Foundations of mathematics/Applied mathematics
• Research Institution: The University of Electro-Communications
• Principal Investigator: Nishiyama Yu 電気通信大学, 大学院情報理工学研究科, 助教 (60586395)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: カーネル法 / カーネルベイズ推論 / 無限分解可能分布 / 畳み込み無限分解可能カーネル / 共役カーネル / 畳み込みトリック / 安定分布 / 一般化双曲型分布

Outline of Final Research Achievements

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.

Free Research Field

機械学習、応用数学