Seth Sohan, Príncipe José C
Helsinki Institute for Information Technology HIIT, Department of Information and Computer Science, Aalto University, Espoo, Finland.
Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA.
Int J Bioinform Res Appl. 2014;10(1):43-58. doi: 10.1504/IJBRA.2014.058777.
Mutual information, conditional mutual information and interaction information have been widely used in scientific literature as measures of dependence, conditional dependence and mutual dependence. However, these concepts suffer from several computational issues; they are difficult to estimate in continuous domain, the existing regularised estimators are almost always defined only for real or vector-valued random variables, and these measures address what dependence, conditional dependence and mutual dependence imply in terms of the random variables but not finite realisations. In this paper, we address the issue that given a set of realisations in an arbitrary metric space, what characteristic makes them dependent, conditionally dependent or mutually dependent. With this novel understanding, we develop new estimators of association, conditional association and interaction association. Some attractive properties of these estimators are that they do not require choosing free parameter(s), they are computationally simpler, and they can be applied to arbitrary metric spaces.
互信息、条件互信息和交互信息在科学文献中已被广泛用作依赖性、条件依赖性和相互依赖性的度量。然而，这些概念存在几个计算问题；它们在连续域中难以估计，现有的正则化估计器几乎总是仅针对实值或向量值随机变量定义，并且这些度量解决的是随机变量方面的依赖性、条件依赖性和相互依赖性意味着什么，而不是有限的实现。在本文中，我们解决了这样一个问题：给定任意度量空间中的一组实现，是什么特征使它们具有依赖性、条件依赖性或相互依赖性。基于这种新颖的理解，我们开发了关联、条件关联和交互关联的新估计器。这些估计器的一些吸引人的特性是它们不需要选择自由参数，计算更简单，并且可以应用于任意度量空间。
