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The Exact VC Dimension of the WiSARD -Tuple Classifier.

Hugo C C Carneiro1, Carlos E Pedreira2, Felipe M G França3

  • 1Programa de Engenharia de Sistemas e Computação, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-972, Brazil hcesar@cos.ufrj.br.

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Summary

This study determines the exact VC dimension for the WiSARD (Wilkie, Stonham, and Aleksander recognition device) -tuple classifier and its bleaching extension. The findings confirm the bleaching technique enhances generalization without compromising performance.

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Area of Science:

  • Machine Learning
  • Artificial Intelligence
  • Neural Networks

Background:

  • The Wilkie, Stonham, and Aleksander recognition device (WiSARD) -tuple classifier is a weightless neural network known for single-step learning.
  • A key challenge for WiSARD classifiers is RAM node saturation with large datasets, prompting research into mitigation techniques like the bleaching extension.

Purpose of the Study:

  • To theoretically determine the exact VC dimension of the basic two-class WiSARD -tuple classifier.
  • To determine the exact VC dimension of the bleaching extension of the WiSARD -tuple classifier.
  • To analyze the impact of the bleaching technique on the WiSARD classifier's generalization capability.

Main Methods:

  • Derivation of the exact VC dimension for the basic WiSARD -tuple classifier.
  • Calculation of the exact VC dimension for the WiSARD classifier with the bleaching extension.
  • Theoretical analysis comparing the VC dimensions of both models.

Main Results:

  • The exact VC dimension of the basic WiSARD -tuple classifier is determined to be linearly proportional to the number of RAM nodes and exponentially related to the tuple length.
  • The VC dimension of the bleaching extension is found to be identical to that of the basic WiSARD -tuple classifier.
  • Empirical results indicate the bleaching extension achieves high accuracy with low variance.

Conclusions:

  • The bleaching technique is confirmed as an enhancement to the WiSARD -tuple classifier, as it does not negatively impact the generalization capability.
  • The theoretical findings support the practical effectiveness of the bleaching extension in improving WiSARD classifier performance.