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Mathematical Genetics in Post Genome Era

后基因组时代的数学遗传学

基本信息

批准号：
14540104
负责人：
MASE Shigeru
金额：
$ 1.28万
依托单位：
TOKYO INSTITUTE OF TECHNOLOGY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540104/
关键词：
Bayesian network LBP algorithm linkage analysis MAPP estimator credit-rating Cayley tree phase transition learning theory Belief Propagation Unwrappedネットワークマルコフ確率場相転移バウンダリ確率則 Loopy Belief Propagation マーカー遺伝子ゲノム解析遺伝連鎖解析

项目摘要

Stochastic networks with and without are common frameworks in many genetical problems. In particular, They are basis of linkage analysis of family genetic data. The LBP (Loopy Belief Propagation) algorithm is an efficient algorithm for estimating marginal probabilities of nodes of stochastic networks with loops. In order to apply this algorithm to linkage analysis, we studied the following basic theoretical problem :(1)Taking Cayley trees as examples, convergence and marginal probability recovery problems were studied. Using theoretical and numerical results, we show that the convergence is closely related with the existence of phase transitions. Ising models on Cayley trees have two kind of phase transitions. LBP converges on one phase transition region, but does not converge on another phase transition region. If converged, beliefs may not coincide with true marginal probabilities. Nevertheless, it is observed that states that both give highest values are coincide.(2)As an application of stochastic networks, we consider an application of credit-rating of companies. It is shown that a naive Bayesian networks can give better predictions than common subjective networks employed by analysts.(3)With an applications to bioinformatics in mind, Kanamori studied some properties of learning theory. In particular, boosting methods.

有无随机网络是许多遗传问题的共同框架。特别是，它们是家系遗传数据连锁分析的基础。LBP(Loopy Believe Propagation)算法是一种估计有环随机网络节点边际概率的有效算法。为了将该算法应用于连锁分析，我们研究了以下基本理论问题：(1)以Cayley树为例，研究了收敛问题和边际概率恢复问题。利用理论和数值结果，我们证明了收敛与相变的存在密切相关。Cayley树上的Ising模型有两种相变。LBP在一个相变区收敛，但在另一个相变区不收敛。如果是一致的，信念可能与真实的边际概率不一致。然而，观察到两者给出最高值的状态是一致的。(2)作为随机网络的应用，我们考虑了公司信用评级的一个应用。结果表明，朴素贝叶斯网络比分析员常用的主观网络能够给出更好的预测。(3)考虑到生物信息学的应用，Kanamori研究了学习理论的一些性质。特别是助推方法。