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@iraedeus iraedeus commented Oct 13, 2025

This pull request significantly improves the documentation and mathematical rigor of the EM algorithm and method of moments sections in the math notes. The main changes include expanding the explanation of the method of moments, clarifying the connection between EM steps and weighted data, adding detailed references to authoritative sources, and improving bibliography formatting and completeness.

Documentation and Mathematical Explanations:

  • Expanded the moments.tex document with detailed sections on the EM algorithm's E-step, weighted empirical moments, component-wise optimization, and a worked example for mixtures of normal distributions. This adds clarity on how the method of moments is applied to mixture models, particularly in the context of the EM algorithm.

References and Citations:

  • Added explicit references to equations from McLachlan & Peel (2000) throughout the q_function.tex file, improving traceability and academic rigor for likelihood, log-likelihood, and Q-function derivations. [1] [2]
  • Added a note in the Q-function section that EM algorithm iterations via Q-function optimization are equivalent to log-likelihood optimization, citing the original Dempster et al. paper.

Bibliography Improvements:

  • Updated the bibliography entry for McLachlan & Peel (2000) to use consistent formatting and added missing fields. Added a new entry for Dempster et al. (1977), the foundational EM algorithm paper, with full metadata and DOI.

Formatting and Minor Enhancements:

  • Added a new font family for Cyrillic monospaced text in packages.tex to improve typesetting.
  • Ensured bibliography is printed at the end of relevant documents for completeness.

These changes collectively enhance the clarity, academic reliability, and usability of the mathematical documentation for mixture models and the EM algorithm.

@iraedeus iraedeus self-assigned this Oct 13, 2025
@iraedeus iraedeus linked an issue Oct 13, 2025 that may be closed by this pull request
@iraedeus iraedeus added the documentation Improvements or additions to documentation label Oct 13, 2025
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DOCS: add documentation about moments method

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