例如对于平面上的点,使用所有直线为假设集合时,VC 维为 3,因为只要 3 个点不共线就可以,而 4 个点形成矩形且相邻点不同的情况就是反例。证明 VC 维往往需要我们为其构造一个解,同时证明大于的情况都是不可行的。 记VCdim(H)=dVCdim(H)=d,现在我们可以用 Sauer's lemma 为 Growth function 给出组合...
· g_S 表示g_S (单个函数在样本集上)与随机噪声 \sigma 的相关性(correlation);而取上确界的动作,则表示函数族 G 在样本集上与随机噪声 \sigma 的相关性(correlation);最后取期望的动作,则表示函数族 G 在样本集上与随机噪声相关性的平均水平(Thus, the empirical Rademacher complexity measures on average...
2. Rademacher Complexity and VC-Dimension The sample complexity bounds above are restricted to finite hypothesis sets. This section gives learning guarantees for infinite hypothesis sets. loss function L:\mathcal{Y}\times\mathcal{Y}\rightarrow\mathbb{R} family of loss functions \mathcal{G}=...
VC-Dimension和Rademacher complexity是机器学习中常提到的度量复杂的的概念,一直远观而没有亵玩,今天对这个概念进行学习记录。 VC-Dimension 全称为Vapnik-Chervonenkis dimension,从wiki上搞来一段定义 InVapnik–Chervonenkis theory, theVapnik–Chervonenkis (VC) dimensionis a measure of the capacity (complexity, ex...
Foundations of Machine Learning: Rademacher complexity and VC-Dimension(1)前面两篇文章中,我们在给出PAC-learnable定理时,都有一个前提假设,那就是 Hypothesis set 是有限的。但很明显,在实际中的假设集大都是无限的,比如上一篇文章中介绍的与坐标轴对齐的矩阵的例子,其 Hypothesis set 就是无限的。
VC-Dimension和Rademacher complexity是机器学习中常提到的度量复杂的的概念,一直远观而没有亵玩,今天对这个概念进行学习记录。 VC-Dimension 全称为Vapnik-Chervonenkis dimension,从wiki上搞来一段定义 InVapnik–Chervonenkis theory, theVapnik–Chervonenkis (VC) dimensionis a measure of the capacity (complexity, ex...
本文主要向大家介绍了VC编程之Foundataions of Machine Learning: Rademacher complexity and VC-Dimension,通过具体的内容向大家展示,希望对大家学习VC编程有所帮助。 (一) 增长函数(Growth function) 在引入增长函数之前,我们先介绍一个例子,这个例子会有助于理解增长函数这个东西。
In the references,Rademacher complexity instead of VC dimension as a measure of the complexity of the learning model and also the risk of learning has been given.Basing on these,discussed the Rademacher kernel Hilbert space,obtains the bound of the risk of support vector machine,which is about ...
Rademacher Complexity Ashish Rastogi 1 Introduction • In a learning task, there is a relationship between • complexity of the class of functions • learning algorithm’s generalizability • Measures of complexity of a class of functions: • VC dimension, VC entropy • Covering numbers, ...
We considerVC dimension|( Error bound|( several complexity measures which capture the difficulty of learning under theI.i.d. datadoi:10.1007/978-3-319-21852-6_6Vladimir V. V’yuginSpringer International PublishingV Yugin V V. VC dimension, fat-shattering dimension, Rademacher averages, and ...