practical_n.py

import numpy as np
from joblib import Parallel, delayed
from tqdm.auto import tqdm

from histogramEstimator import HistogramEstimator
from truncatedGaussian import TruncatedGaussian
from truncatedLaplace import TruncatedLaplace

a, b = 0, 1
runs = 100
laplace_parameters = [
    (
        0.5,
        {"D": 9.25, "C": 4.63, "epsilon": 2.00, "gamma": 0.5, "delta": 0.95},
    ),
    (
        0.8,
        {"D": 4.38, "C": 2.19, "epsilon": 1.25, "gamma": 0.3, "delta": 0.95},
    ),
    (
        1.0,
        {"D": 3.16, "C": 1.58, "epsilon": 1.00, "gamma": 0.2, "delta": 0.95},
    ),
    (
        2.0,
        {"D": 1.27, "C": 0.64, "epsilon": 0.5, "gamma": 0.1, "delta": 0.95},
    ),
    (
        5.0,
        {"D": 0.44, "C": 0.22, "epsilon": 0.2, "gamma": 0.05, "delta": 0.95},
    ),
]

gaussian_parameters = [
    (
        0.3,
        {"D": 7.06, "C": 5.40, "epsilon": 5.56, "gamma": 1.4, "delta": 0.95},
    ),
    (
        0.5,
        {"D": 2.42, "C": 2.03, "epsilon": 2.00, "gamma": 0.5, "delta": 0.95},
    ),
    (
        0.6,
        {"D": 1.62, "C": 1.49, "epsilon": 1.39, "gamma": 0.3, "delta": 0.95},
    ),
    (
        1.0,
        {"D": 0.54, "C": 0.70, "epsilon": 0.50, "gamma": 0.1, "delta": 0.95},
    ),
    (
        2.0,
        {"D": 0.13, "C": 0.23, "epsilon": 0.13, "gamma": 0.05, "delta": 0.95},
    ),
]

rdp_laplace_parameters = [
    (
        1.5,
        {"D": 1.83, "C": 0.913, "epsilon": 0.143, "gamma": 0.04, "delta": 0.95},
    ),
    (
        2.0,
        {"D": 1.27, "C": 0.64, "epsilon": 0.082, "gamma": 0.02, "delta": 0.95},
    ),
    (
        3.0,
        {"D": 0.78, "C": 0.4, "epsilon": 0.037, "gamma": 0.01, "delta": 0.95},
    ),
    (
        5.0,
        {"D": 0.44, "C": 0.22, "epsilon": 0.013, "gamma": 0.004, "delta": 0.95},
    ),
]

rdp_gaussian_parameters = [
    (
        1.5,
        {"D": 0.23, "C": 0.38, "epsilon": 0.016, "gamma": 0.004, "delta": 0.95},
    ),
    (
        2.0,
        {
            "D": 0.13,
            "C": 0.23,
            "epsilon": 0.0052,
            "gamma": 0.002,
            "delta": 0.95,
        },
    ),
    (
        3.0,
        {
            "D": 0.056,
            "C": 0.11,
            "epsilon": 0.001,
            "gamma": 0.0003,
            "delta": 0.95,
        },
    ),
    (
        5.0,
        {
            "D": 0.02,
            "C": 0.04,
            "epsilon": 0.00013,
            "gamma": 0.00005,
            "delta": 0.95,
        },
    ),
]

all_experiments = [
    (TruncatedLaplace, False, laplace_parameters),
    (TruncatedGaussian, False, gaussian_parameters),
    (TruncatedLaplace, True, rdp_laplace_parameters),
    (TruncatedGaussian, True, rdp_gaussian_parameters),
]


file = "results/results.csv"
with open(file, "w") as f:
    f.write(
        "mechanism,a,b,delta,gamma,runs,scale,epsilon,D,C,k,m,n_th,n_pr,renyi\n"
    )

n_exp = sum(len(params_list) for _, _, params_list in all_experiments)
with tqdm(total=n_exp) as pbar:
    for mechanism_class, is_rdp, params_list in all_experiments:
        for scale, params in params_list:
            print(
                f"\n{mechanism_class.__name__}, {'RDP, ' if is_rdp else ''}scale={scale}, D={params['D']}, C={params['C']}, epsilon={params['epsilon']}, gamma={params['gamma']}"
            )

            mechanism = mechanism_class(a=a, b=b, scale=scale)
            estimator = HistogramEstimator(
                mechanism=mechanism,
                a=a,
                b=b,
                C=params["C"],
                D=params["D"],
                epsilon=params["epsilon"],
                delta=params["delta"],
                gamma=params["gamma"],
                renyi=is_rdp,
                alpha=2.0,
                verbose=False,
            )
            n_th = estimator.n
            m = estimator.m
            if not m:
                estimator.m = int(np.ceil(100 / estimator.gamma))

            n_pr = 1
            while True:
                estimator.n = n_pr
                valid = 0
                n_res = 0
                if n_pr > 1e7:
                    n_jobs = 10
                    prefer = "processes"
                else:
                    n_jobs = -1
                    prefer = "threads"
                for estimate in Parallel(
                    n_jobs=n_jobs, return_as="generator", prefer=prefer
                )(delayed(estimator.estimate)(0, 1) for _ in range(runs)):
                    error = abs(estimate - estimator.epsilon)
                    n_res += 1
                    if error <= estimator.gamma:
                        valid += 1
                    pbar.set_description(
                        f"n = {n_pr:.2g}, run = {n_res}/{runs}, valid_ratio = {valid / n_res:.2g} (need > {estimator.delta}), error = {error:.2g} (need < {estimator.gamma})"
                    )
                if valid / runs >= estimator.delta:
                    break
                n_pr *= 2

            result = [
                mechanism.__class__.__name__.replace("Truncated", ""),
                a,
                b,
                estimator.delta,
                estimator.gamma,
                runs,
                scale,
                params["epsilon"],
                params["D"],
                params["C"],
                estimator.k if estimator.k is not None else "Und.",
                m if m is not None else "Und.",
                f"{n_th:.1g}" if n_th is not None else "Und.",
                f"{n_pr:.1g}",
                is_rdp,
            ]
            with open(file, "a") as f:
                f.write(",".join(str(i) for i in result) + "\n")
            pbar.update(1)