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摘要翻译：
本文基于I.I.D.给出了R\'Enyi熵和互信息的简单且计算效率高的非参数估计。从$\r^d$上未知的绝对连续分布中提取的样本。估计量分别以样本的广义最近邻图和样本的经验copula的边的欧几里得长度的p次方之和计算。我们首次证明了这些估计的几乎肯定相合性及其收敛速度的上界，后者是在样本下的密度为Lipschitz连续的假设下得到的。实验证明了它们在独立子空间分析中的有效性。
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英文标题：
《Estimation of R\'enyi Entropy and Mutual Information Based on
Generalized Nearest-Neighbor Graphs》
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作者：
D\'avid P\'al, Barnab\'as P\'oczos, Csaba Szepesv\'ari
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最新提交年份：
2010
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分类信息：
一级分类：Statistics 统计学
二级分类：Machine Learning 机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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一级分类：Computer Science 计算机科学
二级分类：Artificial Intelligence 人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
We present simple and computationally efficient nonparametric estimators of R\'enyi entropy and mutual information based on an i.i.d. sample drawn from an unknown, absolutely continuous distribution over $\R^d$. The estimators are calculated as the sum of $p$-th powers of the Euclidean lengths of the edges of the `generalized nearest-neighbor' graph of the sample and the empirical copula of the sample respectively. For the first time, we prove the almost sure consistency of these estimators and upper bounds on their rates of convergence, the latter of which under the assumption that the density underlying the sample is Lipschitz continuous. Experiments demonstrate their usefulness in independent subspace analysis.
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PDF链接：
https://arxiv.org/pdf/1003.1954
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