用深度学习估算连续变量间互信息，效果优于传统方法。
Towards a pretrained deep learning estimator of the Linfoot informational correlation
- 基于高斯与克雷顿拷贝函数的真值标签训练模型
- 相比核密度、K近邻等方法，偏差和方差更低
- 适合需要高效准确互信息估计的研究者
我们提出一种监督式深度学习方法，用于估计两个连续随机变量间的互信息。标签采用具有优良性质的林福特信息相关性（Linfoot informational correlation），即互信息的变换形式。模型基于高斯与克雷顿拷贝函数的真值标签进行训练。与基于核密度、K近邻及神经网络的估计器相比，本方法表现出更低的偏差与方差。作为概念验证，未来研究可尝试在更多类型拷贝函数（如其他具有真值标签的拷贝函数）上训练模型，以提升泛化能力。
原文摘要 · Abstract (English)
We develop a supervised deep-learning approach to estimate mutual information between two continuous random variables. As labels, we use the Linfoot informational correlation, a transformation of mutual information that has many important properties. Our method is based on ground truth labels for Gaussian and Clayton copulas. We compare our method with estimators based on kernel density, k-nearest neighbours and neural estimators. We show generally lower bias and lower variance. As a proof of principle, future research could look into training the model with a more diverse set of examples from other copulas for which ground truth labels are available.
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