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Effectiveness of Kullback-Leibler Information As A Measure of Dependence

Kullback-Leibler 信息作为依赖性衡量标准的有效性

基本信息

批准号：
12480063
负责人：
SHIBATA Ritei
金额：
$ 6.66万
依托单位：
Keio University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

项目摘要

The aim of this project is to investigate effectiveness of Kullback-Leibler information. In this project, various aspects of this information measure have been investigated.We could show the effectiveness of Kullback-Leibler information as a criterion of model selection. It is clarified that Bootstrap type estimate of Kullback-Leibler information is quite powerful, particularly in case of discrete distributions like Binomial or Multinomial.To ensure practical usefulness of model selection technique based on Kullback-Leibler information, we performed various type of real data analysis, In due course of analysis of interest rate time series, we found that neural network should be included in a family of statistical models to be selected. We then extended ordinary neural network to stochastic neural network and developed an efficient training algorithm. We also gave a mathematical proof of the convergence. The stochastic neural network is quite powerful, for example, it gives us the best one day ahead prediction of fall or rise of TOPIX with around 60% accuracy.We also analyzed satellite radar received signals and instantaneous foreign exchange prices to investigate effectiveness of Kullback-Leibler information as a criterion for the processing. As a result, we found ten times precise data processing algorithm for the former and constructed a clustered Poisson marked process for the latter.To investigate information flows on graphical model, we concentrated our attention into conditional independence which is a key idea in graphical modeling. As a result, we found that conditional independence is too strong condition to be realized unless in case of normal distribution or its monotone transformed distribution. However, we found that Kullback-Leibler information is a promising alternative measure in place of conditional independence.

该项目的目的是研究Kullback-Leibler信息的有效性。在这个项目中，我们已经研究了这个信息测度的各个方面，我们可以证明Kullback-Leibler信息作为模型选择标准的有效性。为了保证基于Kullback-Leibler信息的模型选择技术的实用性，我们进行了各种类型的真实的数据分析，在利率时间序列分析的适当过程中，我们发现，神经网络应该包括在一个家庭的统计模型进行选择。然后将普通神经网络推广到随机神经网络，并提出了一种有效的训练算法。并给出了收敛性的数学证明。随机神经网络的功能非常强大，例如，它可以提前一天预测TOPIX的下跌或上涨，准确率约为60%。我们还分析了卫星雷达接收信号和瞬时外汇价格，以研究Kullback-Leibler信息作为处理标准的有效性。在此基础上，我们为前者找到了10倍精度的数据处理算法，为后者构造了一个聚类Poisson标记过程。为了研究图模型上的信息流，我们将注意力集中在图建模中的一个关键思想--条件独立性上。结果发现，条件独立性是一个很强的条件，除非是正态分布或其单调变换分布，否则很难实现。然而，我们发现，Kullback-Leibler信息是一个有前途的替代措施的地方条件独立。