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Related Experiment Video

Updated: Sep 13, 2025

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Hyperparameter Optimization EM Algorithm via Bayesian Optimization and Relative Entropy.

Dawei Zou^1,2, Chunhua Ma¹, Peng Wang^1,2

¹School of Information Engineering, Suihua University, Suihua 152061, China.

Entropy (Basel, Switzerland)

|July 29, 2025

Summary

Hyperparameter optimization (HPO) effectively tunes machine learning models using an EM algorithm derived from evidence maximization. This method demonstrates fast convergence for relevance vector machines and Bayesian linear regression.

Keywords:

EM algorithm evidence function hyperparameters optimization relative entropy

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Area of Science:

Machine Learning
Statistical Modeling

Background:

Hyperparameter optimization (HPO) is crucial for machine learning model performance.
Hyperparameters regulate algorithm behavior and are not learned from training data.

Purpose of the Study:

To derive iterative equations for hyperparameter optimization using evidence function maximization.
To provide a mathematical and statistical explanation for hyperparameter reestimation.

Main Methods:

Utilized zero-mean Gaussian weight priors for relevance vector machine hyperparameter optimization.
Derived iterative reestimation equations for hyperparameters in Bayesian linear regression.
Applied relative entropy and Bayesian optimization to partition equations into E and M steps.

Main Results:

Demonstrated the effectiveness of the EM algorithm for hyperparameter optimization.
The algorithm exhibited fast convergence.
A singular covariance matrix in the posterior distribution affected likelihood increase.

Conclusions:

The EM algorithm is effective for hyperparameter optimization, offering fast convergence.
Further research may address the impact of singular covariance matrices on model likelihood.