A circular-linear dependence measure under Johnson-Wehrly distributions and its application in Bayesian networks
A circular-linear dependence measure under Johnson-Wehrly distributions and its application in Bayesian networks
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Johnson-Wehrly 分布下的循环线性相关性测度及其在贝叶斯网络中的应用
DOI：
10.1016/j.ins.2019.01.080
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发表时间：
2019
影响因子：
8.1
通讯作者：
Concha Bielza and Shogo Kato
中科院分区：
文献类型：
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作者：
Ignacio Leguey;Pedro Larranaga;Concha Bielza and Shogo Kato
与线性数据联合观测的圆形数据在不同学科中很常见。由于圆形数据需要不同于线性数据的技术，对圆形和线性观测的联合数据使用通常的相关性度量往往具有误导性。此外，尽管存在循环变量之间的互信息度量，但该度量的缺点在于它仅定义为包裹的柯西分布的二元扩展，并且必须使用数值方法来逼近。在本文中，我们引入了两个相关性度量，即(I)圆-线性互信息作为圆和线性变量之间相关性的度量；(Ii)圆-圆互信息作为两个循环变量之间相关性的度量。结果表明，对于Johnson-Wehrly分布的子族，所提出的圆线性互信息的表达式可以大大简化。我们应用这两个相关性度量来学习一个结合了循环变量和线性变量的圆线性树形结构贝叶斯网络。为了说明和评估我们的建议，我们用模拟数据进行了实验。我们还使用了来自不同欧洲站的真实气象数据集来创建环状线性树形结构的贝叶斯网络模型。
Circular data jointly observed with linear data are common in various disciplines. Since circular data require different techniques than linear data, it is often misleading to use usual dependence measures for joint data of circular and linear observations. Moreover, although a mutual information measure between circular variables exists, the measure has drawbacks in that it is defined only for a bivariate extension of the wrapped Cauchy distribution and has to be approximated using numerical methods. In this paper, we introduce two measures of dependence, namely, (i) circular-linear mutual information as a measure of dependence between circular and linear variables and (ii) circular-circular mutual information as a measure of dependence between two circular variables. It is shown that the expression for the proposed circular-linear mutual information can be greatly simplified for a subfamily of Johnson–Wehrly distributions. We apply these two dependence measures to learn a circular-linear tree-structured Bayesian network that combines circular and linear variables. To illustrate and evaluate our proposal, we perform experiments with simulated data. We also use a real meteorological data set from different European stations to create a circular-linear tree-structured Bayesian network model.