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Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data01:16

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Measuring Statistical Learning Across Modalities and Domains in School-Aged Children Via an Online Platform and Neuroimaging Techniques
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Statistical guarantees for regularized neural networks.

Mahsa Taheri1, Fang Xie1, Johannes Lederer1

  • 1Department of Mathematics, Ruhr-University Bochum, Universitätsstraße 150, 44801 Bochum, Germany.

Neural Networks : the Official Journal of the International Neural Network Society
|May 17, 2021
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Summary

This study provides a general statistical guarantee for learning neural networks using regularized estimators. The findings offer a mathematical basis for deep learning, improving understanding of neural network generalization.

Keywords:
Deep learningNeural networksPrediction guaranteesRegularization

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Area of Science:

  • Machine Learning
  • Statistics
  • Computer Science

Background:

  • Neural networks are widely used for data analysis but lack robust mathematical theories.
  • Existing statistical guarantees for learning neural networks are limited, especially for practical estimators.

Purpose of the Study:

  • To develop a general statistical guarantee for neural network estimators.
  • To provide a mathematical foundation for regularized estimation in deep learning.

Main Methods:

  • Developed a general statistical guarantee for estimators combining a least-squares term and a regularizer.
  • Applied and exemplified the guarantee using ℓ1-regularization.

Main Results:

  • The prediction error of ℓ1-regularized neural networks grows logarithmically with the number of parameters.
  • Prediction error can decrease as the number of layers in the neural network increases.

Conclusions:

  • Established a mathematical basis for regularized estimation of neural networks.
  • Deepened the mathematical understanding of neural networks and deep learning principles.