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Performance-guaranteed regularization in maximum likelihood method: Gauge symmetry in Kullback-Leibler divergence.

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  • 1Department of Applied Mathematics, Faculty of Science, Fukuoka University, 8-19-1, Nanakuma, Jonan-ku, Fukuoka City 814-0180, Japan.

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Summary

This study introduces a novel regularization method for maximum likelihood estimation, inspired by error-correcting codes and gauge symmetry. It achieves optimal probability models without hyperparameter tuning, addressing overfitting in data analysis.

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Area of Science:

  • Statistics
  • Information Theory
  • Machine Learning

Background:

  • Maximum likelihood estimation (MLE) is a standard method for estimating probability models from data.
  • Conventional MLE can lead to overfitting by creating models too close to the empirical distribution.
  • Regularization methods aim to prevent overfitting, but their systematic performance is not well understood.

Purpose of the Study:

  • To propose a theoretically guaranteed regularization method for maximum likelihood estimation.
  • To leverage gauge symmetry in Kullback-Leibler divergence for improved model performance.
  • To eliminate the need for frequent hyperparameter searches in regularization.

Main Methods:

  • The study draws parallels between regularization and error-correcting codes, particularly the role of gauge symmetry in optimal decoding.
  • A novel regularization technique is developed for MLE by applying principles of gauge symmetry to Kullback-Leibler divergence.
  • The proposed method integrates gauge symmetry to achieve optimal model selection.

Main Results:

  • The developed regularization method provides theoretical guarantees for optimal model selection.
  • The approach successfully prevents overfitting without relying on empirical distribution fitting.
  • The method eliminates the necessity of hyperparameter tuning, a common challenge in regularization.

Conclusions:

  • The proposed gauge symmetry-based regularization offers a principled and effective alternative to conventional methods.
  • This approach enhances the robustness and reliability of probability models estimated via MLE.
  • The elimination of hyperparameter search simplifies the application of regularization in statistical modeling.