# Local Bias Correction versus Global Synchronization in Distributed Maximum Likelihood

Authors listed in the working paper: Simon-Pierre Boucher and GPT-6.1 (AI designation requested by the user).

This is a working research note, not a peer-reviewed or priority-validated paper. The theorem assumptions, limits of the exponential illustration, and computational scope are explained inside the PDF.

# Files

• pamle.tex - LaTeX source (16-page article)
• references.bib - machine-readable bibliography (the article also contains manual bibliography entries, so BibTeX is not required for compilation)
• figures/mc_comparison.pdf - vector chart included in the article
• figures/mc_comparison.png - preview version of the chart
• monte_carlo.py - exact-Gamma reproducible simulation
• simulation_summary.csv - reported statistics for 500 replications per partition count
• simulation_replicates.csv - 10,500 method/replication rows, across 3 designs x 500 replications x 7 estimators

# Build the LaTeX article

pdflatex -interaction=nonstopmode pamle.tex
pdflatex -interaction=nonstopmode pamle.tex

Requirements: pdfLaTeX and standard LaTeX packages (amsmath, amsthm, microtype, hyperref, cleveref, natbib, tikz, listings, etc.). The project uses relative paths, so compile from this directory.

# Reproduce Monte Carlo

pip install numpy matplotlib
python monte_carlo.py

Seed: 20261028. Total observations in each replication: 1,048,576. Partition sizes: m=256, m=64, m=16. Repetitions: 500 per design. Exponential rate=1. The script draws exact block-wise Gamma sufficient statistics rather than materializing every individual observation.

No physical cluster was benchmarked and no numerical speedup is claimed. All simulations are synthetic and measure scaled estimator gaps relative to the centralized MLE.