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The Exact VC Dimension of theWiSARD n-Tuple Classifier

机译：WiSARD n元组分类器的精确VC维

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摘要

The Wilkie, Stonham, and Aleksander recognition device (WiSARD) n-tuple classifier is a multiclass weightless neural network capable of learning a given pattern in a single step. Its architecture is determined by the number of classes it should discriminate. A target class is represented by a structure called a discriminator, which is composed of N RAM nodes, each of them addressed by an n-tuple. Previous studies were carried out in order to mitigate an important problem of the WiSARD n-tuple classifier: having its RAM nodes saturated when trained by a large data set. Finding the VC dimension of the WiSARD n-tuple classifier was one of those studies. Although no exact value was found, tight bounds were discovered. Later, the bleaching technique was proposed as a means to avoid saturation. Recent empirical results with the bleaching extension showed that the WiSARD n-tuple classifier can achieve high accuracies with low variance in a great range of tasks. Theoretical studies had not been conducted with that extension previously. This work presents the exact VC dimension of the basic two-class WiSARD n-tuple classifier, which is linearly proportional to the number of RAM nodes belonging to a discriminator, and exponentially to their addressing tuple length, precisely N(2n-1)+1. The exact VC dimension of the bleaching extension to the WiSARD n-tuple classifier, whose value is the same as that of the basic model, is also produced. Such a result confirms that the bleaching technique is indeed an enhancement to the basic WiSARD n-tuple classifier as it does no harm to the generalization capability of the original paradigm.
机译：Wilkie，Stonham和Aleksander识别设备（WiSARD）n元组分类器是一种多类失重神经网络，能够在单个步骤中学习给定模式。它的体系结构由应区分的类数决定。目标类由称为鉴别器的结构表示，该结构由N个RAM节点组成，每个节点由一个n元组寻址。为了减轻WiSARD n元组分类器的一个重要问题，进行了先前的研究：当通过大数据集训练时，其RAM节点饱和。这些研究之一是找到WiSARD n元组分类器的VC维。尽管没有找到确切的值，但发现了严格的界限。后来，提出了漂白技术作为避免饱和的手段。最近的关于漂白扩展的经验结果表明，WiSARD n元组分类器可以在许多任务中以较低的方差实现较高的精度。以前没有对该扩展进行过理论研究。这项工作提出了基本的两类WiSARD n元组分类器的确切VC维度，它与属于一个鉴别器的RAM节点的数量成线性比例，并与它们的寻址元组长度成指数关系，精确地为N（2n-1）+ 1。还生成了WiSARD n元组分类器的漂白扩展的精确VC维度，该值与基本模型的值相同。这样的结果证实了该漂白技术确实是对基本WiSARD n元组分类器的增强，因为它不会损害原始范例的泛化能力。

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  • 来源
    《Neural computation》 |2019年第1期|176-207|共32页
  • 作者

    Carneiro Hugo C. C.; Pedreira Carlos E.; Franca Felipe M. G.; Lima Priscila M. V.;

  • 作者单位

    Univ Fed Rio de Janeiro, Programa Engn Sistemas & Comp, BR-21941972 Rio De Janeiro, Brazil;

    Univ Fed Rio de Janeiro, Programa Engn Sistemas & Comp, BR-21941972 Rio De Janeiro, Brazil;

    Univ Fed Rio de Janeiro, Programa Engn Sistemas & Comp, BR-21941972 Rio De Janeiro, Brazil;

    Univ Fed Rio de Janeiro, Inst Tercio Pacitti Aplicacoes & Pesquisas Comp, BR-21941916 Rio De Janeiro, Brazil;

  • 收录信息 美国《科学引文索引》(SCI);美国《化学文摘》(CA);
  • 原文格式 PDF
  • 正文语种 eng
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