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Related Experiment Videos

SMEM algorithm is not fully compatible with maximum-likelihood framework.

Akihiro Minagawa¹, Norio Tagawa, Toshiyuki Tanaka

¹Graduate School of Engineering, Tokyo Metropolitan University, Hachioji, Tokyo, 192-0397 Japan. akihiro@eei.metro-u.ac.jp

Neural Computation

|May 22, 2002

Summary

The Split-and-Merge Expectation-Maximization (SMEM) algorithm can improve mixture model analysis. This study shows comparing log likelihoods guarantees increased model fit, unlike its previous acceptance-rejection method.

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Area of Science:

Machine Learning
Statistical Modeling
Computational Statistics

Background:

The standard Expectation-Maximization (EM) algorithm can converge to local optima in mixture models.
The Split-and-Merge Expectation-Maximization (SMEM) algorithm was proposed to address this limitation by incorporating nonlocal search operations.

Purpose of the Study:

To analyze the evaluation method used in the SMEM algorithm.
To demonstrate a method for guaranteeing an increase in model likelihood during mixture model optimization.

Main Methods:

Critique of the acceptance-rejection evaluation within the SMEM algorithm.
Theoretical demonstration of likelihood improvement through log-likelihood comparisons.

Main Results:

Related Experiment Videos

The acceptance-rejection method in SMEM may select distributions with lower likelihood.
Comparing log likelihoods ensures a guaranteed increase in the model's likelihood function.

Conclusions:

The SMEM algorithm's reliance on acceptance-rejection can be suboptimal.
Directly comparing log likelihoods provides a robust approach to enhance mixture model fitting.