def __init__(self, b=None, name='Laplace', RDP_off=False, phi_off=True):
"""
b: the ratio of the scale parameter and L1 sensitivity.
RDP_off: if False, then we characterize the mechanism using RDP.
fdp_off: if False, then we characterize the mechanism using fdp.
phi_off: if False, then we characterize the mechanism using phi-function.
"""
Mechanism.__init__(self)
self.name = name
self.params = {'b': b} # This will be useful for the Calibrator
self.delta0 = 0
if not phi_off:
log_phi_p = lambda x: phi_bank.phi_laplace(self.params, x)
log_phi_q = lambda x: phi_bank.phi_laplace(self.params, x)
self.log_phi_p = log_phi_p
self.log_phi_q = log_phi_q
self.propagate_updates((log_phi_p, log_phi_q), 'log_phi')
if not RDP_off:
new_rdp = lambda x: rdp_bank.RDP_laplace({'b': b}, x)
self.propagate_updates(new_rdp, 'RDP')
def __init__(self, b=None, name='Laplace'):
Mechanism.__init__(self)
self.name = name
self.params = {'b': b} # This will be useful for the Calibrator
self.delta0 = 0
if b is not None:
new_rdp = lambda x: rdp_bank.RDP_laplace({'b': b}, x)
self.propagate_updates(new_rdp, 'RDP')
def get_eps_laplace(b, delta):
assert (delta >= 0)
func = lambda x: rdp_bank.RDP_laplace({'b': b}, x)
return get_eps_rdp(func, delta)
def get_moment(alpha, sigma, gamma):
t = 3
part_1 = gamma**2*alpha/((1-gamma)*sigma**2)
part_2 = (2*gamma)**t/((1-gamma)**t*sigma**(2*t))
part_3 = (2*gamma)**t*(t-1)/(2*(1-gamma)**(t-1)*sigma**t)
part_4 = (2*prob)**t*np.exp((t**2-t)/(2*sigma**2))*(sigma**t*2+t**t)/(2*(1-gamma)**(t-1)*sigma**(2*t))
bound = part_1 + alpha*(alpha-2)/6*(part_2+part_3+part_4)
part_sum = 4 * alpha * (alpha - 2) * gamma ** 3 / (3 * sigma ** 3)
return bound
# get the CGF functions
func_gaussian = lambda x: rdp_bank.RDP_gaussian({'sigma': sigma}, x)
func_laplace = lambda x: rdp_bank.RDP_laplace({'b': b}, x)
func_randresp = lambda x: rdp_bank.RDP_randresponse({'p':p}, x)
func_moment = lambda x: get_moment({'gamma':prob,'sigma':sigma},x)
funcs = { 'gaussian':func_gaussian,'laplace': func_laplace, 'randresp': func_randresp}
# A placeholder to save results for plotting purposes
results_for_figures = {}
# compute feasible alpha list for moment account in Abadi et. al.2016
moment =[]
moment_alpha =np.linspace(1, alpha_limit, alpha_limit).astype(int)
for mm in moment_alpha:
moment.append(get_moment(mm, sigma, prob))
moment_cache = np.zeros(alpha_limit)
moment = np.array(moment)
def get_eps_moment(alpha,cache):