PLD-subsampling 0.1.3

PLD PMF/PLD transformations: subsampling amplification and infinity-mass scaling utilities

PLD_subsampling

Implements and evaluates privacy amplification by subsampling for Privacy Loss Distribution (PLD) probability mass functions (PMFs). Generates CDF plots and epsilon ratio plots comparing analytical ground truth, dp-accounting, and our direct subsampling implementation.

Package layout

• PLD_subsampling/
  • PLD_subsampling_impl.py: Core subsampling primitives
    • stable_subsampling_loss: numerically stable loss mapping
    • exclusive_ccdf_from_pdf: CCDF helper (exclusive tail)
    • subsample_losses: transforms a PMF on a uniform loss grid
  • wrappers/dp_accounting_wrappers.py: Thin wrappers around dp-accounting (construct PLDs, amplify PLDs separately for remove/add), plus PMF/PLD utilities
    • amplify_pld_separate_directions(base_pld, sampling_prob) -> PrivacyLossDistribution: returns a PLD with amplified remove/add PMFs
    • scale_pmf_infinity_mass(pmf, delta) -> PMF: increases the infinity mass by delta and scales all finite probabilities by (1-β-δ)/(1-β) preserving PMF type (dense/sparse)
    • scale_pld_infinity_mass(pld, delta) -> PrivacyLossDistribution: applies the same infinity-mass change to both directions of a PLD and returns a new PLD
  • testing/
    • analytic_Gaussian.py: Analytical PLD and epsilon(δ) formulas for Gaussian mechanism
    • test_utils.py: Experiment runners (run_experiment, run_multiple_experiments)
    • plot_utils.py: Plotting (CDF with focused x-range, epsilon ratio)
  • main.py: Runs experiments and saves figures to plots/

Quickstart

1. Create a virtual environment and install dependencies

python3 -m venv .venv
source .venv/bin/activate
python -m pip install --upgrade pip
pip install -r requirements.txt

2. Editable install for local development (optional)

pip install -e .

3. Run experiments and generate plots

python -m PLD_subsampling.main

Figures are written to plots/ (treat this directory as build output).

Usage examples

Scale infinity mass on a PMF and a PLD (see PLD_subsampling/example.ipynb for a full demo):

from PLD_subsampling.wrappers.dp_accounting_wrappers import (
    scale_pmf_infinity_mass,
    scale_pld_infinity_mass,
)
from dp_accounting.pld import privacy_loss_distribution

# Build a fresh PLD
pld = privacy_loss_distribution.from_gaussian_mechanism(
    standard_deviation=1.0,
    sensitivity=1.0,
    value_discretization_interval=1e-4,
    sampling_prob=0.1,
    pessimistic_estimate=True,
)

# Scale a single PMF
pmf_scaled = scale_pmf_infinity_mass(pld._pmf_remove, delta=1e-4)

# Scale both directions of the PLD
pld_scaled = scale_pld_infinity_mass(pld, delta=1e-4)

Notes

• CDF plots automatically focus the main x-axis on the transition region and add slight y-padding to show the 0 and 1 limits clearly.
• Epsilon-ratio plots show method/GT vs analytical epsilon over log-scale epsilon.
• All heavy computations use vectorized NumPy operations with careful numerical handling in tail regions.

Build a package

python -m pip install --upgrade build
python -m build

Artifacts will be created under dist/. To upload to PyPI/TestPyPI, use twine with an API token.