(1)引入relative entropy和mutual information的定义。 (2)揭示entropy, relative entropy, 以及mutual information的关系和性质。 (3)介绍data-processing inequality、sufficient statistics以及Fano's inequality。 2.1 RELATIVE ENTROPY AND MUTUAL INFORMATON
Entropy, relative entropy and mutual information. Entropy H(X)=−∑xp(x)logp(x),H(X)=−∑xp(x)logp(x), 熵非负, 且当且仅当XX确定性的时候为有最小值0, 即P(X=x0)=1P(X=x0)=1. Proof: 由loglog的凹性可得 H(X)=−∑xp(x)logp(x)=∑xp(x)log1p(x)≥log1=0.H(X...
1.EntropyandMutualInformation 第一章熵和互信息 1.1Discreterandomvariables 离散随机变量 SupposeXisadiscreterandomvariable,thatis,onewhoserangeR={x1,x2,}isfiniteorcountable.Letpi={X=xi}.TheentropyofXisdefinedby 假设X是一个离散随机变量，取值范围R={x1,x2,…}是有限的或可数的。设pi=p{X=xi}...
Entropy and mutual information in models of deep neural networks* We examine a class of stochastic deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold... Marylou Gabri茅,Andre Manoel,Cl茅ment Luneau,... - 《Journal of Statisti...
Entropy, mutual information, and relative entropy are work horses in Shannon theoretic analyses for communications and compression. These quantities have already been utilized in the analyses of agent learning and the exploration of structure in sequences. This chapter provides concise treatments of ...
Entropy and Mutual Information 来自 Springer 喜欢 0 阅读量: 3 作者: JD Gibson 摘要: Entropy, mutual information, and relative entropy are work horses in Shannon theoretic analyses for communications and compression. These quantities have already been utilized in the analyses of agent learning and ...
Mutual information is one of many quantities that measures how much one random variables tells us about another. It is a dimensionless quantity with (generally) units of bits, and can be thought of as the reduction in uncertainty about one random variable given knowledge of another.[1] ...
在前三篇文章中,我们深入探讨了信息论的基础概念——从信息熵的本质(Entropy and Shannon Entropy),到联合熵和条件熵(Joint and Conditional Entropy)的复杂交织,再到互信息和信息增益(Mutual Information and Information Gain)在数据处理和决策中的重要应用。这些概念为我们提供了理解信息如何被量化和处理的基础。现在...
Mutual information (MI), an information theory statistic, explicitly quantifies diagnostic uncertainty by measuring information gain before vs after diagnostic testing. In this paper, we propose the use of MI as a single measure to express diagnostic test performance and demonstrate how it can be ...
Another important measurement is called Mutual Information. It is a measure of mutual dependency among two variables. One way to define it is the loss of entropy(uncertainty) when given a condition:另一个重要的衡量标准是相互信息。它是两个变量之间相互依赖性的度量。定义它的一种方法是在给定条件时...