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Mathematical modeling for high-dimensional nonlinear data and its application to the analysis of complex phenomena

高维非线性数据的数学建模及其在复杂现象分析中的应用

基本信息

批准号：
13440034
负责人：
KONISHI Sadanori
金额：
$ 7.49万
依托单位：
KYUSHU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13440034/
关键词：
Nonlinear modeling Bayesian model selection criterion Radial basis function Classification and Discrimination Functional data analysis Nonlinear time series analysis Diffusion process Regularized basis expansions 非線形基底展開ノンパラメトリックグラフィカルモ

项目摘要

In recent years the wide availability of fast and inexpensive computers enables us to accumulate a huge amount of data, and the effective use of databases are required in order to create innovation and values and to solve important science and engineering problems. Statistical challenges posed by large data sets arise in such areas as genome databases in life science, remote-sensing data from earth observing satellites, POS data in marketing and economic data. Through this research project we have investigated the problem of constructing various types of statistical nonlinear modeling strategies and obtained the results in the following :(1)We proposed nonlinear modeling techniques ; determining a set of basis functions, estimating the unknown parameters by regularization and then evaluating the constructed model to select a suitable one among competing models. We describe modeling based on functional approach and introduce a generalized information criterion. Bayesian information criterion BIC is also extended in such a way that it can be applied to the evaluation of models estimated by the method of regularization.(2)We proposed functional regression modeling and functional discriminant analysis, using Gaussian radial basis functions along with the technique of regularization. The proposed method was applied to the analysis of yeast cell cycle gene expression data.(3)Approximate selection of embedding dimension and delay time have been a central issue of chaotic dynamical systems. We introduced the delay time and consider the estimation of embedding dimension and delay time.(4)Model selection criteria were presented for stochastic process from an information-theoretic approach. We derived asymptotic expansions for the distributions of statistics related to small diffusions and applied it to option pricing in economics.

近年来，快速而廉价的计算机的广泛使用使我们能够积累大量的数据，有效地使用数据库是创造创新和价值以及解决重要科学和工程问题所必需的。在生命科学中的基因组数据库、地球观测卫星的遥感数据、营销中的POS数据和经济数据等领域，大型数据集带来了统计挑战。通过本课题的研究，我们研究了各种统计非线性建模策略的构造问题，取得了以下成果：（1）提出了非线性建模技术，确定一组基函数，通过正则化估计未知参数，然后对所构造的模型进行评价，在竞争模型中选择合适的模型。我们描述了建模的基础上功能的方法，并介绍了一个广义的信息准则。本文还对贝叶斯信息准则BIC进行了推广，使其可以应用于正则化方法估计的模型的评价。(2)We提出了函数回归建模和函数判别分析，使用高斯径向基函数沿着与正则化技术。将该方法应用于酵母细胞周期基因表达数据的分析。（3）嵌入维数和延迟时间的近似选取一直是混沌动力系统研究的热点问题。我们引入延迟时间，并考虑嵌入维数和延迟时间的估计。（4）从信息论的角度给出了随机过程的模型选择准则。我们导出了与小扩散相关的统计分布的渐近展开式，并将其应用于经济学中的期权定价。