基本图和贝叶斯网络

IF 2.6 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Systems Science & Complexity Pub Date : 2008-11-08 DOI:10.1109/CANS.2008.25

Angel Garrido

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引用次数: 3

摘要

我们在本文中的目的是展示如何在计算意义上获得用于学习贝叶斯网络(lbn)的改进工具。并给出一个数学上更一致和完整的公式。首先，通过划分等价类，然后选择一个图作为每一个等价类的代表，即所谓的基本图。其次，分析当节点数趋于无穷时，等价类(本质图)的基数与n阶有向无环图(dag)的基数之比的渐近行为，以及相互间的渐近行为。这项研究是用代数和几何方法进行的。最后，我们描述了未来的研究方向，在lbn和概率图形模型(PGMs)中，利用新的代数和几何工具。

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Essential Graphs and Bayesian Networks

Our purpose in this paper is to show how it is possible to obtain improved tools, in a computational sense, for Learning Bayesian Networks (LBNs). And also give a more mathematically consistent and complete formulation. First, by the partition in equivalence classes, and then selecting a graph as representative of each one of them, the so called Essential Graph. Second, analyzing the asymptotical behavior of the ratio among the cardinal of equivalence classes (therefore, of essential graphs) and the cardinal of Directed Acyclic Graphs (DAGs) of order n, and reciprocally, when this number of nodes tends to infinity. This study is made in both algebraic and geometrical ways. Finally, we describe the future research lines, in LBNs and Probabilistic Graphical Models (PGMs), by new algebraic and geometrical tools.

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来源期刊

Journal of Systems Science & Complexity 数学-数学跨学科应用

CiteScore

3.80

自引率

9.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Systems Science and Complexity is dedicated to publishing high quality papers on mathematical theories, methodologies, and applications of systems science and complexity science. It encourages fundamental research into complex systems and complexity and fosters cross-disciplinary approaches to elucidate the common mathematical methods that arise in natural, artificial, and social systems. Topics covered are: complex systems, systems control, operations research for complex systems, economic and financial systems analysis, statistics and data science, computer mathematics, systems security, coding theory and crypto-systems, other topics related to systems science.