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Related Experiment Videos

Empirical error-confidence curves for neural network and Gaussian classifiers

G J Wolff1, D G Stork, A Owen

  • 1Machine Learning & Perception Group, Ricoh California Research Center, Menlo Park, CA 94025, USA. wolff@crc.ricoh.com

International Journal of Neural Systems
|July 1, 1996
PubMed
Summary

This study empirically tests Probably Almost Bayes (PAB) theory for classifier error-confidence. PAB bounds are conservative, and linear predictions align with linear discriminant performance but not neural networks.

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Area of Science:

  • Machine Learning
  • Statistical Learning Theory
  • Computational Statistics

Background:

  • Error-Confidence (EC) quantifies classifier error probability relative to Bayes error.
  • Probably Almost Bayes (PAB) theory models EC increase with training data.
  • Understanding classifier performance scaling is crucial for practical applications.

Purpose of the Study:

  • Empirically investigate the relationship between training samples and classifier error-confidence.
  • Evaluate the predictive accuracy of PAB bounds and asymptotic statistics.
  • Compare performance of linear classifiers versus neural networks.

Main Methods:

  • Generated Error-Confidence (EC) curves by varying the number of training patterns (m).
  • Compared empirical results with theoretical predictions from PAB and asymptotic statistics.

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  • Utilized linear classifiers and neural networks on Gaussian problems.

    • Main Results:

    • PAB bounds were found to be highly conservative on Gaussian problems.
    • Asymptotic statistics predictions showed good agreement with linear discriminant performance at low Bayes error rates.
    • A linear relationship between log average error and log training patterns was observed, but with deviations from theory for neural networks and higher error rates.

    Conclusions:

    • PAB theory provides conservative bounds for classifier error-confidence.
    • Linear classifier performance aligns with asymptotic predictions under certain conditions.
    • Neural network performance exhibits greater dependence on classifier capacity, challenging simple linear scaling predictions.