lattice theoryThe Vapnik–Chervonenkis (V–C) dimension of a set of functions representing a feed-forward, multi-layered, single output artificial neural network (ANN) with hard-limited activation functions can be evaluated using the Poincaré polynomial of the implied hyperplane arrangement. This ANN...
VC维(Vapnik–Chervonenkis dimension) 1、简介 vc理论(Vapnik–Chervonenkis theory )是由 Vladimir Vapnik 和 Alexey Chervonenkis发明的。该理论试图从统计学的角度解释学习的过程。而VC维是VC理论中一个很重要的部分。 2、定义 定义:对一个指示函数集,如果存在h个样本能够被函数集中的函数按所有可能的 种形式分开,...
\(\mathcal{F}\) 的 Vapnik–Chervonenkis Dimension,简称 VC Dimension,记作 \(d_\mathcal{F}\),是最大的满足如下条件的整数 \(N\) \[ S_\mathcal{F}(N) = 2^N \] 如果不存在这样的整数,我们记 \(d_\mathcal{F}=\infty\)。 显然...
The foundation of this principle is the fact that the error rate of the learning machine on test data is confined by the sum of training error rate and a term that depends on the Vapnik–Chervonenkis (VC) dimension [60]. In the SVM theory, different types of kernel functions can be ...
定义2 (Vapnik–Chervonenkis Dimension) F 的 Vapnik– Chervonenkis Dimension,简称 VC Dimension,记作 d F ,是最 大的满足如下条件的整数N S F (N) = 2 N 如果不存在这样的整数,我们记d F =∞。 显然所有大于d F 的整数都是F 的break point。VC 维的重要性在于 它刻画了F的“复杂度”,这一点我们...
In machine learning theory, the Vapnik-Chervonenkis dimension or VC-dimension of a concept class is the cardinality of the largest set which can be shattered by . If arbitrarily large sets can be shattered by , then the VC-dimension is said to be ...
Vapnik Chervonenkis dimension is a basic combinatorial notion with applications in machinelearning, stability theory, and statistics. We explore what effect modeltheoretic structure has on the VC dimension of formulas, considered asparameterized families of sets, with respect to long disjunctions and...
doi:10.1007/978-1-4612-0711-5_13Luc DevroyeLászló GyrfiGábor LugosiDevroye, L.; Gyorfi, L.; Lugosi, G. Vapnik-Chervonenkis theory. In A Probabilistic Theory of Pattern Recognition; Springer: New York, NY, USA, 1996; pp. 187-213....
Lecture 18 : Introduction to Vapnik-Chervonenkis ( VC ) Theory Vapnik-Chervonenkis TheoryCastro, R
Vapnik-Chervonenkis dimensionclassifiersThe paper introduces some generalizations of Vapnik's (1982) method of structural risk minimization (SRM). As well as ... J Shawe-Taylor,PL Bartlett,RC Williamson,... - 《Information Theory IEEE Transactions on》 被引量: 104发表: 1998年 Evaluating the Vapn...