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.

作为用于分析图形传播算法的一种新数学方法，已经提出了一种新型的图Zeta函数，用于分析循环信念传播算法，并用于揭示比已知的更强的理论结果。同样，已经提出了一种循环扩展的方法来分析循环信念传播的近似误差。作为期望传播的数学基础，基于正定的内核和其估计方法和理论特性已被研究。

项目成果

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.

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

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

Statistical Mechanical Analysis of Low-Density Parity-Check Codes on General Markov Channel

通用马尔可夫信道低密度奇偶校验码的统计力学分析

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

Kernel Method for Bayesian Inference

贝叶斯推理的核方法

• 发表时间: 2010
• 作者: Kentaro Inoue;Shin Shimozono;Hideaki Yoshida;Sayaka Tomeda;Kazuya Fukami;Shinpei Tonami;Hiroyuki Kurata;福水健次
• 通讯作者: 福水健次