Kernel Bayes Inference and Infinitely Divisible Distributions

• 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
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• 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 / 正定値カーネル / 特性的カーネル / カーネル平均 / カーネルベイズ / 一般化双曲系型分布 / Convolution Trick / セミパラメトリックカーネルベイズ / Levy Khintchine公式

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.

Research Products

• [Int'l Joint Research] ジョージア工科大学(米国)
• [Int'l Joint Research] University College London(英国)
• [Int'l Joint Research] Georgia Institute of Technology(米国)
• [Journal Article] Characteristic Kernels and Infinitely Divisible Distributions (2016)
  • Author(s): Yu Nishiyama and Kenji Fukumizu
  • Journal Title: Journal of Machine Learning Research Volume: 17 Pages: 1-28
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] The Nonparametric Kernel Bayes Smoother (2016)
  • Author(s): Yu Nishiyama, Amir Hossein Afsharinejad, Shunsuke Naruse, Byron Boots, Le Song
  • Journal Title: The 19th International Conference on Artificial Intelligence and Statistics (AISTATS 2016) Volume: - Pages: 547-555
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Filtering with State-Observation Examples via Kernel Monte Carlo Filter (2016)
  • Author(s): Motonobu Kanagawa, Yu Nishiyama, Arthur Gretton, and Kenji Fukumizu
  • Journal Title: Neural Computation Volume: 28 Issue: 2 Pages: 382-444
  • DOI: 10.1162/neco_a_00806
  • Peer Reviewed / Int'l Joint Research
• [Presentation] The Nonparametric Kernel Bayes Smoother (2016)
  • Author(s): Yu Nishiyama, Amir Hossein Afsharinejad, Shunsuke Naruse, Byron Boots, Le Song
  • Organizer: The 19th International Conference on Artificial Intelligence and Statistics (AISTATS 2016)
  • Place of Presentation: Cadiz, Spain
  • Year and Date: 2016-05-09
  • Int'l Joint Research
• [Presentation] Nonparametric Kernel Bayes Smoothing on State Space Models (2016)
  • Author(s): 西山悠
  • Organizer: 新学術領域研究「スパースモデリングの深化と高次元データ駆動科学の創成」2015年度公開シンポジウム
  • Place of Presentation: 神戸
  • Year and Date: 2016-03-07
• [Presentation] kNNを用いたカーネルベイズの計算量削減法の検討 (2015)
  • Author(s): 苗村智行, 都築俊介, 西山悠
  • Organizer: 第18回情報論的学習理論ワークショップ(IBIS2015)
  • Place of Presentation: 筑波大学，茨城
  • Year and Date: 2015-11-26
• [Presentation] カーネルベイズスムージングとカーネル平均Toolboxの作成 (2015)
  • Author(s): 西山悠
  • Organizer: 第25回日本神経回路学会全国大会(JNNS 2015)
  • Place of Presentation: 電気通信大学, 東京
  • Year and Date: 2015-09-04
• [Presentation] Nonparametric Smoothing on State Space Models with Kernel Mean Embeddings (2015)
  • Author(s): Yu Nishiyama, Amir Hossein Afsharinejad, Shunsuke Naruse, Byron Boots, Le Song
  • Organizer: STM2015 & CSM2015
  • Place of Presentation: The Institute of Statistical Mathematics, Tokyo
  • Year and Date: 2015-07-15
  • Int'l Joint Research
• [Presentation] Nonparametric Smoothing on State Space Models with Kernel Mean Embeddings (2015)
  • Author(s): Yu Nishiyama, Amir Hossein Afsharinejad, Shunsuke Naruse, Byron Boots, Le Song
  • Organizer: 1st Symposium on Intelligent Systems in Science and Industry (SISSI)
  • Place of Presentation: Max Planck Institute, Tuebingen
  • Year and Date: 2015-07-12
  • Int'l Joint Research
• [Presentation] Model-based Kernel Sum Rule with Applications to State Space Models (2014)
  • Author(s): Yu Nishiyama, Motonobu Kanagawa, Arthur Gretton, Kenji Fukumizu
  • Organizer: The Neural Information Processing Systems (NIPS) Workshop: ABC in Montreal
  • Place of Presentation: Canada
  • Year and Date: 2014-12-12
• [Presentation] カーネル法と確率分布の無限分解可能性 (2014)
  • Author(s): 西山悠
  • Organizer: 日本応用数理学会 2014年度年会
  • Place of Presentation: 政策研究大学院大学
  • Year and Date: 2014-09-05
• [Presentation] Monte Carlo Filtering using Kernel Embedding of Distributions (2014)
  • Author(s): Motonobu Kanagawa, Yu Nishiyama, Arthur Gretton, and Kenji Fukumizu
  • Organizer: 28th AAAI Conference on Artificial Intelligence
  • Place of Presentation: Canada
  • Year and Date: 2014-07-27 – 2014-07-31
• [Remarks] Yu Nishiyama
  • URL: https://sites.google.com/site/ynishiyam/research
• [Remarks]
  • URL: https://sites.google.com/site/ynishiyam/home
• [Remarks]
  • URL: http://www.is.uec.ac.jp/staff/list/ss/nishiyama-yu.html
• [Remarks] GoogleSites
  • URL: https://sites.google.com/site/ynishiyam/home
• [Remarks] 電気通信大学大学院情報システム学研究科
  • URL: http://www.is.uec.ac.jp/staff/list/ss/nishiyama-yu.html
• [Remarks] ResearchMap
  • URL: http://researchmap.jp/YuNishiyama/