Mathematical foundation of efficient algorithms for statistical inference

统计推断高效算法的数学基础

• 批准号: 22300098
• 负责人: FUKUMIZU Kenji
• 金额: $ 7.82万
• 依托单位: The Institute of Statistical Mathematics
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22300098/
• 关键词: グラフ; アルゴリズム; 確率計算; 情報幾何; 位相幾何

As a new mathematical method for analyzing propagation algorithms on graphs, a novel Graph zeta function has been proposed for the analysis of the loopy belief propagation algorithm, and used for revealing stronger theoretical results than the known ones. Also, a method of loop expansion has been proposed for analyzing the approximation error of the loopy belief propagation.As a mathematical foundation of the expectation propagation, an infinite dimensional exponential family has been proposed based on positive definite kernels, and its estimation methods and theoretical properties have been studied.

作为一种新的分析图上传播算法的数学方法，提出了一种新的Graph zeta函数，用于分析循环置信传播算法，并揭示了比已知算法更强的理论结果.提出了一种循环展开方法来分析循环置信传播的逼近误差，并基于正定核提出了一种无限维指数族，作为期望传播的数学基础，研究了它的估计方法和理论性质.

项目成果

Kernel Bayes’ Rule and its Applications.

核贝叶斯规则及其应用。

• 发表时间: 2012
• 作者: Yuko Ito;Takashi Yoshidome;Nobuyuki Matubayashi;Masahiro Kinoshita;Mitsunori Ikeguchi;Kenji Fukumizu
• 通讯作者: Kenji Fukumizu

Kernel and Feature Search in Kernel PCA

内核 PCA 中的内核和特征搜索

• 发表时间: 2011
• 作者: Alam;A.;Fukumizu;K.
• 通讯作者: K.

Cavity approach to dense random linear equations

稠密随机线性方程的空腔方法

• 发表时间: 2011
• 作者: 樺島祥介

(2013) Equivalence of distance-based and RKHS-based statistics in hypothesis testing,,

(2013) 假设检验中基于距离和基于 RKHS 的统计的等效性，

• 发表时间: 2013
• 期刊: Annals of Statistics
• 影响因子: 4.5
• 作者: Sejdinovic;D.;Sriperumbudur;B.;Gretton;A. and Fukumizu;K.
• 通讯作者: K.

Kernel Bayes' rule: Bayesian inference with positive definite kernels

• DOI: 10.5555/2567709.2627677
• 发表时间: 2013
• 期刊: J. Mach. Learn. Res.
• 作者: K. Fukumizu;Le Song;A. Gretton