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muffliato.py
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muffliato.py
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from copy import deepcopy
from graphutils import contrib, vplambda
import numpy as np
import networkx as nx
from tqdm import tqdm, trange
def gamma_tcheb(lambda2):
"""Compute the factor gamma in the tchebychev polynomials for the acceleration
Parameters
----------
lambda2: float,
second smallest eigenvalue of the Laplacian
Returns
-------
gamma: float
"""
return 2 * (1 - np.sqrt(lambda2 * (1 - lambda2/4))) / (1 - lambda2/2)**2
def simulation(graph, T, n, sigma=1, u=0, debug=False, approx=False, alpha=2):
"""Run muffliato without Tchebychev acceleration
Parameters
----------
graph: networkx graph
T: int
number of gossip steps
n: int
number of nodes
sigma: float
u: int
fixed node for the computation of privacy
debug: boolean, default: False
print the gossip matrix
approx: boulean, default: False
compute the formula given in corollary 1
gamma: float, default: None
the gamma constant for Tchebychev polynomials, when not given it is computed as define in Algorithm 1
alpha: float
parameter of RDP
Returns
-------
eps_inst: array, shape(T, nb of nodes)
the privacy loss per step for each node
error: array, shape (T,)
the convergence of x towards the mean
proba_2: array, shape (T, number of nodes)
privacy loss when approx is used
precision: float
magnitude of the difference between the true and the noisy version. going below this precision is not meaningful
"""
np.random.seed(1)
contribution = np.zeros(n) # array to stock the contribution of a neighbor
eps_inst = np.zeros((T, n)) # privacy loss due to iteration t in node i
error = np.zeros(T)
x_inst = np.zeros((T+1,n))
x_exact = np.random.uniform(size=n)
x_inst[0] = np.clip(x_exact + np.random.randn(n) * sigma, 0, 1)
#x_exact = np.array([n]+[0]*(n-1))
print("x", x_exact)
#x_inst[0] = np.clip(x_exact + np.random.randn(n) * sigma, 0, 1)
x_mean_exact = np.mean(x_exact)
x_mean = np.mean(x_inst[0])
precision = (x_mean - x_mean_exact)**2
print("precision", precision)
W = nx.to_numpy_array(graph)
if debug:
print("the gossip matrix", W)
if approx:
proba_2 = np.zeros((T, n))
Wt = deepcopy(W)
for t in trange(T):
for v in nx.nodes(graph):
contribution[v] = alpha * contrib(Wt, u, v) / (2 * sigma**2)
if approx:
proba_2[t][v] = Wt[u][v]**2
for v in nx.nodes(graph):
for w in nx.neighbors(graph, v):
if w != v:
eps_inst[t][v] += contribution[w]
x_inst[t+1] = W @ x_inst[t]
error[t] = np.linalg.norm(x_inst[t]-x_mean)**2 /n
Wt = W @ Wt
if approx:
return eps_inst, error, proba_2, precision
return eps_inst, error, precision
def acceleratedsimulation(graph, T,n, sigma, u=0, debug=False, approx=False, gamma=None, alpha=2):
"""Run muffliato
Parameters
----------
graph: networkx graph
T: int
number of gossip steps
n: int
number of nodes
sigma: float
u: int
fixed node for the computation of privacy
debug: boolean, default: False
print the gossip matrix
approx: boulean, default: False
compute the formula given in corollary 1
gamma: float, default: None
the gamma constant for Tchebychev polynomials, when not given it is computed as define in Algorithm 1
alpha: float
parameter of RDP
Returns
-------
eps_inst: array, shape(T, nb of nodes)
the privacy loss per step for each node
error: array, shape (T,)
the convergence of x towards the mean
proba_2: array, shape (T, number of nodes)
privacy loss when approx is used
precision: float
magnitude of the difference between the true and the noisy version. going below this precision is not meaningful
"""
np.random.seed(0)
if gamma is None:
lambda2 = vplambda(graph)
gamma = gamma_tcheb(lambda2)
print("Gamma ", gamma, "for a lambda ", lambda2)
contribution = np.zeros(n) # array to stock the contribution of a neighbor
eps_inst = np.zeros((T, n)) # privacy loss due to iteration t in node i
error = np.zeros(T) #
x_inst = np.zeros((T+1,n))
x_exact = np.random.uniform(size=n)
x_inst[0] = np.clip(x_exact + np.random.randn(n) * sigma, 0, 1)
x_mean_exact = np.mean(x_exact)
x_mean = np.mean(x_inst[0])
precision = (x_mean - x_mean_exact)**2
W = nx.to_numpy_array(graph)
if debug:
print("the gossip matrix", W)
if approx:
proba_2 = np.zeros((T, n))
Wt = deepcopy(W)
for t in trange(T):
for v in nx.nodes(graph):
contribution[v] = contrib(Wt, u, v)
if approx:
proba_2[t][v] = Wt[u][v]**2
for v in nx.nodes(graph):
for w in nx.neighbors(graph, v):
if w != v:
eps_inst[t][v] += contribution[w]
if t == 0:
x_inst[t+1] = W @ x_inst[t]
else:
x_inst[t+1] = gamma * W @ x_inst[t] + (1 - gamma) * x_inst[t-1]
error[t] = np.linalg.norm(x_inst[t]-x_mean)**2 /n
Wt = W @ Wt
if approx:
return eps_inst, error, proba_2, precision
return eps_inst, error, precision
def gossip_vector(theta_init, graph, T):
"""
Compute the result of a gossip for a vector theta instead of a single real
Parameters
----------
theta_init : array, shape (n_nodes, p)
The model parameters in each node at the beginning of the gossip
graph: networkx graph
Graph of commincation, with weights already computed
T: int
Number of gossip steps
Returns
-------
theta: array, shape (n_n)
"""
n, p = theta_init.shape
theta = deepcopy(theta_init)
W = nx.to_numpy_array(graph)
lambda2 = vplambda(graph)
gamma = gamma_tcheb(lambda2)
for idx in range(p):
x_new, x_old = theta[:, idx], np.zeros(n)
for t in range(T):
x_old, x_new = x_new, gamma * W @ x_new + (1 - gamma) * x_old
theta[:, idx] = x_new
return theta