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woodyx218 2020-01-22 10:29:25 +08:00 committed by GitHub
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tensorflow_privacy/privacy/analysis/gdp_accountant.py
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@ -30,32 +30,32 @@ from scipy import optimize
# Target delta:delta
def compute_mu_uniform(epoch, noise_multi, N, batch_size):
'''Compute mu from uniform subsampling'''
'''Compute mu from uniform subsampling.'''
T = epoch*N/batch_size
c = batch_size*np.sqrt(T)/N
return np.sqrt(2)*c*np.sqrt(np.exp(noise_multi**(-2))*\
norm.cdf(1.5/noise_multi)+3*norm.cdf(-0.5/noise_multi)-2)
def compute_mu_Poisson(epoch, noise_multi, N, batch_size):
'''Compute mu from Poisson subsampling'''
def compute_mu_poisson(epoch, noise_multi, N, batch_size):
'''Compute mu from Poisson subsampling.'''
T = epoch*N/batch_size
return np.sqrt(np.exp(noise_multi**(-2))-1)*np.sqrt(T)*batch_size/N
def delta_eps_mu(eps, mu):
'''Dual between mu-GDP and (epsilon, delta)-DP'''
'''Compute dual between mu-GDP and (epsilon, delta)-DP.'''
return norm.cdf(-eps/mu+mu/2)-np.exp(eps)*norm.cdf(-eps/mu-mu/2)
def eps_from_mu(mu, delta):
'''inverse Dual'''
'''Compute epsilon from mu given delta via inverse dual.'''
def f(x):
'''reversely solving dual'''
'''Reversely solve dual by matching delta.'''
return delta_eps_mu(x, mu) - delta
return optimize.root_scalar(f, bracket=[0, 500], method='brentq').root
def compute_eps_uniform(epoch, noise_multi, N, batch_size, delta):
'''inverse Dual of uniform subsampling'''
'''Compute epsilon given delta from inverse dual of uniform subsampling.'''
return eps_from_mu(compute_mu_uniform(epoch, noise_multi, N, batch_size), delta)
def compute_eps_Poisson(epoch, noise_multi, N, batch_size, delta):
'''inverse Dual of Poisson subsampling'''
return eps_from_mu(compute_mu_Poisson(epoch, noise_multi, N, batch_size), delta)
def compute_eps_poisson(epoch, noise_multi, N, batch_size, delta):
'''Compute epsilon given delta from inverse dual of Poisson subsampling.'''
return eps_from_mu(compute_mu_poisson(epoch, noise_multi, N, batch_size), delta)