Relative Entropy Measures of Multivariate Dependence
多变量依赖关系的相对熵度量AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要研究通用依赖度量，未明确涉及经济分布效应、网络干扰或其他所列细分方向。
反馈分类问题正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
多变量依赖关系的相对熵度量
- 研究问题
- 如何用相对熵统一度量多变量及条件依赖，使连续、顺序类别与名义类别变量的混合资料也能获得可解释的指标？
- 方法与思路
- 作者对相对熵进行变换或标准化，构造相关、复相关和偏相关的推广，并比较既有依赖指标及研究估计量的渐近性质。
- 材料陈述的贡献
- 摘要称，新度量可适用于混合变量，并补充描述非单调或非线性依赖；给出全类别变量的标准误及连续情形研究纲要。
- 阅读关注点
- 应核对各种变量类型下的标准化与解释、密度或概率估计的影响，以及类别资料标准误和连续资料理论的完成程度。
- 阅读边界
- 依据稿件版本未注明的索引摘要；连续变量情形仅给出研究纲要，具体估计条件与有限样本表现未说明，不能推断刊本变化。
原文摘要
There has been a lot of work on measures of dependence or association for bivariate probability distributions or bivariate data. These measures usually assume that the variables are both continuous or both categorical. In comparison, there is very little work on multivariate or conditional measures of dependence. The purpose of this article is to discuss measures of multivariate dependence and measures of conditional dependence based on relative entropies. These measures are conceptually very general, as they can be used for a set of variables that can be a mixture of continuous, ordinal-categorical, and nominal-categorical variables. For continuous or ordinal-categorical variables, a certain transformation of relative entropy to the interval [0, 1] leads to generalizations of the correlation, multiple-correlation, and partial-correlation coefficients. If all variables are nominal categorical, the relative entropies are standardized to take a maximum of 1 and then transformed so that in the bivariate case, there is a relative reduction in variability interpretation like that for the correlation coefficient. The relative entropy measures of dependence are compared with commonly used bivariate measures of association such as Kendall's τb and Goodman and Kruskal's λ and with measures of dependence based on Pearson's ϕ2 distance. Examples suggest that these new measures of dependence should be useful additional summary values for nonmonotonic or nonlinear dependence. Assuming that the multivariate data are a random sample, the statistical measures of dependence with estimated probability density or mass functions can be studied asymptotically. Standard errors are obtained when all variables are categorical, and an outline of what must be done in the case of all continuous variables is given.