T分布:温良宽厚 命名与源起 “t”,是伟大的Fisher为之取的名字。Fisher最早将这一分布命名为“Student's distribution”,并以“t”为之标记。 Student,则是William Sealy Gosset(戈塞特)的笔名。他当年在爱尔兰都柏林的一家酒厂工作,设计了一种后来被称为t检验的方法来评价酒的质量。因为行业机密,酒厂不 ...
Rademacher 变量是由 Rademacher 分布(Radamacher Distribution)生成的随机变量。Rademacher 分布是一种二项分布的扩展,其取值范围为 [-1,1]。Rademacher 变量的定义可以表示为: X ~ R(n, p) 其中,n 表示样本数量,p 表示正项的概率。Rademacher 变量的期望值为 0,方差为 1。 3.Rademacher 变量的应用 Rademache...
DISTRIBUTION (Probability theory)This paper introduces a new discrete distribution that depends on two parameters. It can be described as a perturbed version of the standard geometric distribution by adding a "random noise" following the Rademacher distribution. Depending on the values of its ...
从增长函数的定义中我们看到,这种度量假说集合的方法相比于拉德马赫尔复杂度,有一个很大的优点——不依赖于数据的分布(Unlike the Rademacher complexity, this measure does not depend on the distribution, it is purely combinatorial)。 使用Massart's lemma将(经验)拉德马赫尔复杂度与增长函数联系起来: ...
注:对随机变量及其取值规律的研究是概率论的核心内容。在上一个小结中,总结了随机变量的概念以及随机变量与事件的联系。这个小结会更加深入的讨论随机变量。 随机变量与事件 随机变量的本质是一种函数(映射关系),在古典概率模型中,“事件和事件的概率”是核心概念;但是在现代概率论中,“随机变量及其取值规律”是核心...
其证明十分复杂,具体推导在 Ball, Haagerup, and Distribution Functions。 将Khintchine-Kahane不等式代入,有: (∑j=1DEξ|∑i=1mξixi,j|p∗)1/p∗≤p∗[∑j=1D(∑i=1mxi,j2)p∗/2]1/p∗ 再注意到 p≥1 时,|x|p 是凸函数(具有sup-additivity),反之则是凹函数(具有sub-additivity),因...
The theoretically well motivated stopping time determination based on Rademacher penalties gives results that are much closer to those attain ed using heuristics based on assumptions on learning curve shape than distribution independent estimates based on VC dimension do. 展开 ...
(X, )be a compact metric space distribution on Z:::X×Y and 一 {z ) 1 pendently drawn according to p(x, ). and Y — R.Let p(x, )be an unknown probability 一{( ,Y )}7- -l(z ∈ X,Y ∈y)be a sample,inde— A main goal of learning theory is the definition of an ...
The theoretically well motivated stopping time determination based on Rademacher penalties gives results that are much closer to those attained using heuristics based on assumptions on learning curve shape than distribution independent estimates based on VC dimension do. 展开 ...
Then, we present the recent researches of Rademacher complexitylearning bounds for independent and identical distribution (i.i.d.) and non-independent and identical distribution (non-i.i.d.). Finally, we discuss the potential issues and possible directions of Rademacher complexities in statistical ...