docs: add moments strategy math doc #73
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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:
moments.texdocument 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:
q_function.texfile, improving traceability and academic rigor for likelihood, log-likelihood, and Q-function derivations. [1] [2]Bibliography Improvements:
Formatting and Minor Enhancements:
packages.texto improve typesetting.These changes collectively enhance the clarity, academic reliability, and usability of the mathematical documentation for mixture models and the EM algorithm.