validate_gaussian.py

# Compute privacy curves for Gaussian mechanism
# cf. https://github.com/microsoft/prv_accountant/blob/main/notebooks/validate-gaussian.ipynb

import matplotlib.pyplot as plt
import numpy as np
from opacus.accountants import create_accountant
from scipy.stats import norm

MAX_COMPOSITIONS = 10_000
NOISE_MULTIPLIER = 100.0
SAMPLING_PROBABILITY = 1.0
DELTA_ERROR = 1e-10


def delta_exact(eps):
    mu = np.sqrt(MAX_COMPOSITIONS) / NOISE_MULTIPLIER
    return norm.cdf(mu / 2 - eps / mu) - np.exp(eps) * norm.cdf(-mu / 2 - eps / mu)


def compute_delta(accountant, eps, eps_error):
    f_n = accountant._get_dprv(eps_error=eps_error, delta_error=DELTA_ERROR)
    delta_lower = f_n.compute_delta_estimate(eps + eps_error) - DELTA_ERROR
    delta_estim = f_n.compute_delta_estimate(eps)
    delta_upper = f_n.compute_delta_estimate(eps - eps_error) + DELTA_ERROR
    return (delta_lower, delta_estim, delta_upper)


if __name__ == "__main__":
    epss = np.linspace(0.1, 5.0, 10)
    accountant = create_accountant("prv")
    accountant.history = [(NOISE_MULTIPLIER, SAMPLING_PROBABILITY, MAX_COMPOSITIONS)]

    delta_01 = [compute_delta(accountant, eps, 0.1) for eps in epss]
    delta_05 = [compute_delta(accountant, eps, 0.5) for eps in epss]
    delta_1 = [compute_delta(accountant, eps, 1.0) for eps in epss]

    f, ax = plt.subplots(figsize=(14, 8))

    ax.fill_between(
        epss,
        [d_low for d_low, _, _ in delta_01],
        [d_high for _, _, d_high in delta_01],
        label="eps_error=0.1",
        alpha=0.1,
    )
    ax.fill_between(
        epss,
        [d_low for d_low, _, _ in delta_05],
        [d_high for _, _, d_high in delta_05],
        label="eps_error=0.5",
        alpha=0.1,
    )
    ax.fill_between(
        epss,
        [d_low for d_low, _, _ in delta_1],
        [d_high for _, _, d_high in delta_1],
        label="eps_error=1.0",
        alpha=0.1,
    )

    ax.plot(epss, delta_exact(epss), color="tab:red", label="Exact")

    ax.set_yscale("log")
    ax.legend()

    f.savefig("privacy-curve.png", dpi=100)