A Review of the Expectation-Maximization Algorithm and its Applications to Mixture Models
Bibliographic record
Abstract
The Expectation-Maximization (EM) algorithm has long been recognized as a powerful tool for approximating the maximum likelihood estimator in parametric models with latent variables.This thesis provides a selective survey of the existing EM literature, spanning from its original formulation in the 1970s to its present-day developments, with the objective of creating a valuable resource for future research.By exploring the evolution of the EM algorithm, we present both earlier and recent results as well as practical applications in mixture models.Chapter 1 serves as a thorough introduction to the EM, contextualizing it within the broader framework of parameter estimation in parametric models with latent variables.In Chapter 2, we study the general convergence properties of the EM; in particular, we present conditions under which the algorithm's fitted iterates converge inside a ball centered around the true parameter of the model.Meanwhile, in Chapter 3, we survey the existing literature on the EM algorithm as it relates to Gaussian mixture models and mixed linear regression models.Finally, in Chapter 4, we conclude with a discussion on important aspects such as initialization, SNR, parameterization, and new research directions for the EM algorithm.By collating the wealth of knowledge available on the EM algorithm, this thesis offers researchers a valuable reference for understanding, applying, and advancing the EM algorithm.i .
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".