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 给出组合形式的上界:ΠH(
本文在介绍对分(dichotomy)时引用了台湾大学林轩田老师的课件,见《机器学习基石-training versus testing》Chapter 3:Rademacher Complexity and VC-Dimension 3.1 Rademacher(拉德马赫尔)复杂度 Rademacher复杂度 我们依然使用 H 表示假设集合(hypothesis set),用 h 表示假说集合中的某一个假说(hypothesis)。
This corollary remarkably shows that growth function only exhibits two types of behavior: exponential growth all the time, or, exponential growth at the beginning and then polynomial growth, where the transition point is exactly the VC-dimension. In the same vein, a generalization bound can be pr...
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。
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。
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...
We consider several complexity measures which capture the difficulty of learning under the i.i.d. assumption. Among these measures are growth function and VC dimension , covering number and fat-shattering dimension, and Rademacher complexity from statistical learning theory. Relationships among these ...
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, ...
VC-Dimension andRademacherComplexity-based bounds VC-Dimension和Rademachercomplexity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In Vapnik–Chervonenkis theory, the Vapnik–Chervonenkis (VC) dimension ...
In this work, we prove new Rademacher complexity (RC) based bounds, which do not require any additional assumptions for achieving a fast convergence rate O(n−1) in the optimistic case and a slow rate O(n−1/2) in the general case. At the same time, they are characterized by ...