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

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.