# 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

```bash
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

```bash
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.