Private β-Models

Implementation and experiments for Mandal & Nandy, "Privacy-Utility Trade-offs for Parameter Estimation in Degree-Heterogeneous Higher-Order Networks": finite-sample minimax rates for differentially private parameter estimation in the r-uniform hypergraph β-model, under both local and central edge differential privacy. A local-DP estimator (discrete Laplace noise on the degree sequence) and a central-DP estimator (noisy gradient descent) are each compared against non-private (MLE and ridge) baselines, on synthetic data (Numerical experiments/) and a real communication network — the Enron email hypergraph (Data analysis/) — matching the paper's own experiments.

Repository layout

Folder	Contents
Numerical experiments/	Synthetic-data experiments: Slurm-launched parameter-recovery and link-prediction trials, aggregated into the paper's plots.
Data analysis/	The same estimators applied to the real Enron email hypergraph for link prediction.

Each folder's README has the detailed layout, run order, and per-file breakdown.

Requirements

pip install -r requirements.txt

Package	Used for
numpy, scipy	Core linear algebra; hypergraph log-likelihood/gradient computations, discrete Laplace and Gaussian noise mechanisms
pandas	Loading/aggregating per-task result CSVs
scikit-learn	Link-prediction metrics (ROC-AUC, F1, average precision, Brier score)
matplotlib	Result plots
jupyter	Running the aggregation and analysis notebooks
tqdm, joblib	Progress bars and parallel replicate sweeps in the prototype notebook (Numerical experiments/vary_eps.ipynb)
numba	Accelerates the 4-uniform hypergraph likelihood in Data analysis/codes/link_prediction_order4.ipynb