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295 | class DeSGLD:
"""Decentralized Stochastic Gradient Langevin Dynamics
Args:
size_w (int): the size of the network
N (int): the size of the array in each it
sigma (float): the variation of the noise
eta (float): the learning rate
T (int): the iteration numbers
dim (int): the dimension of the input data
b (int): the batch size
lam (float): the regularization parameter
x (float): the input data
y (float): the output data
w (float): the weight matrix from the network structure
hv (float): the tuning parameter for the extra algorithm
reg_type (str): the type of regressor used
Returns:
vanila_desgld()
extra_desgld()
"""
def __init__(
self, size_w, N, sigma, eta, T, dim, b, lam, x, y, w, hv, reg_type
):
self.size_w = size_w
self.N = N
self.sigma = sigma
self.eta = eta
self.dim = dim
self.b = b
self.lam = lam
self.x = x
self.y = y
self.w = w
self.hv = hv
self.T = T
self.reg_type = reg_type
def gradient_logreg(self, beta, x, y, dim, lam, b):
"""Gradient function for the logistic regression
Args:
beta: approximation at each node
x: the input data
y: the output data
dim: the dimension of the input data
lam: the regularization parameter
b: the batch size
Returns:
gradient for the the logistic regression
"""
f = np.zeros(dim)
randomList = np.random.randint(0, len(y) - 1, size=int(b))
for item in randomList:
h = 1 / (1 + np.exp(-np.dot(beta, x[item])))
f -= np.dot((y[item] - h), x[item])
f += (2 / lam) * beta
return f
def gradient_linreg(self, beta, x, y, dim, lam, b):
"""Gradient function for the linear regression
Args:
beta: approximation at each node
x: the input data
y: the output data
dim: the dimension of the input data
lam: the regularization parameter
b: the batch size
Returns:
gradient for the the logistic regression
"""
f = np.zeros(dim)
randomList = np.random.randint(0, len(y) - 1, size=int(b))
for i in randomList:
f = f - np.dot((y[i] - np.dot(beta, x[i])), x[i])
f += (2 / lam) * beta
return f
def vanila_desgld(self):
"""Vanila DeSGLD algorithm
Returns:
history_all: contains the approximation from all the nodes
beta_mean_all: contains the mean of the approximation from
all the nodes
"""
# Initialization
if self.reg_type == "logistic":
beta = np.random.normal(
0, self.sigma, size=(self.N, self.size_w, self.dim)
)
else:
beta = np.random.multivariate_normal(
mean=np.zeros(self.dim),
cov=np.eye(self.dim),
size=(self.N, self.size_w),
)
history_all = []
beta_mean_all = []
for t in range(1):
history = np.empty((self.size_w, self.dim, self.N))
beta_mean = np.empty((self.dim, self.N))
for i in range(self.N):
history[:, :, i] = beta[i, :, :]
for j in range(self.dim):
beta_mean[j, :] = np.mean(history[:, j, :], axis=0)
history_all.append(history)
beta_mean_all.append(beta_mean)
# Update
step = self.eta
for t in range(self.T):
for n in range(self.N):
for i in range(self.size_w):
if self.reg_type == "logistic":
g = self.gradient_logreg(
beta[n, i],
self.x[i],
self.y[i],
self.dim,
self.lam,
self.b,
)
temp = np.zeros(self.dim)
for j in range(len(beta[n])):
temp = temp + self.w[i, j] * beta[n, j]
noise = np.random.normal(0, self.sigma, self.dim)
beta[n, i] = (
temp - step * g + math.sqrt(2 * step) * noise
)
else:
g = self.gradient_linreg(
beta[n, i],
self.x[i],
self.y[i],
self.dim,
self.lam,
self.b,
)
temp = np.zeros(self.dim)
for j in range(len(beta[n])):
temp = temp + self.w[i, j] * beta[n, j]
noise = np.random.multivariate_normal(
mean=np.zeros(self.dim), cov=np.eye(self.dim)
)
beta[n, i] = (
temp - step * g + math.sqrt(2 * step) * noise
)
history = np.empty((self.size_w, self.dim, self.N))
beta_mean = np.empty((self.dim, self.N))
for i in range(self.N):
history[:, :, i] = beta[i, :, :]
for j in range(self.dim):
beta_mean[j, :] = np.mean(history[:, j, :], axis=0)
history_all.append(history)
beta_mean_all.append(beta_mean)
return np.array(history_all), np.array(beta_mean_all)
def extra_desgld(self):
"""EXTRA DeSGLD algorithm
Returns:
history_all: contains the approximation from all the nodes
beta_mean_all: contains the mean of the approximation from
all the nodes
"""
# I_n is the identity matrix of the same size as the weight matrix
I_n = np.eye(self.size_w)
h_values = self.hv
history_all = []
beta_mean_all = []
for h in h_values:
# w1 is the weight matrix with the hyperparameter h
w1 = h * I_n + (1 - h) * self.w
# Initialization
if self.reg_type == "logistic":
beta = np.random.normal(
0, self.sigma, size=(self.N, self.size_w, self.dim)
)
else:
beta = np.random.multivariate_normal(
mean=np.zeros(self.dim),
cov=np.eye(self.dim),
size=(self.N, self.size_w),
)
history_all_h = []
beta_mean_all_h = []
for t in range(1):
history = np.empty((self.size_w, self.dim, self.N))
beta_mean = np.empty((self.dim, self.N))
for i in range(self.N):
history[:, :, i] = beta[i, :, :]
for j in range(self.dim):
beta_mean[j, :] = np.mean(history[:, j, :], axis=0)
history_all_h.append(history)
beta_mean_all_h.append(beta_mean)
# Update
step = self.eta
for t in range(self.T):
for n in range(self.N):
for i in range(self.size_w):
if self.reg_type == "logistic":
# Vanila Part
g = self.gradient_logreg(
beta[n, i],
self.x[i],
self.y[i],
self.dim,
self.lam,
self.b,
)
temp = np.zeros(self.dim)
for j in range(len(beta[n])):
temp = temp + w1[i, j] * beta[n, j]
noise = np.random.normal(0, self.sigma, self.dim)
beta[n, i] = (
temp - step * g + math.sqrt(2 * step) * noise
)
# Extra Part
g = self.gradient_logreg(
beta[n, i],
self.x[i],
self.y[i],
self.dim,
self.lam,
self.b,
)
temp = np.zeros(self.dim)
for j in range(len(beta[n])):
temp = temp + self.w[i, j] * beta[n, j]
noise = np.random.normal(0, self.sigma, self.dim)
beta[n, i] = (
temp - step * g + math.sqrt(2 * step) * noise
)
else:
# Vanila Part
g = self.gradient_linreg(
beta[n, i],
self.x[i],
self.y[i],
self.dim,
self.lam,
self.b,
)
temp = np.zeros(self.dim)
for j in range(len(beta[n])):
temp = temp + w1[i, j] * beta[n, j]
noise = np.random.multivariate_normal(
mean=np.zeros(self.dim), cov=np.eye(self.dim)
)
beta[n, i] = (
temp - step * g + math.sqrt(2 * step) * noise
)
# Extra Part
g = self.gradient_linreg(
beta[n, i],
self.x[i],
self.y[i],
self.dim,
self.lam,
self.b,
)
temp = np.zeros(self.dim)
for j in range(len(beta[n])):
temp = temp + self.w[i, j] * beta[n, j]
noise = np.random.multivariate_normal(
mean=np.zeros(self.dim), cov=np.eye(self.dim)
)
beta[n, i] = (
temp - step * g + math.sqrt(2 * step) * noise
)
history = np.empty((self.size_w, self.dim, self.N))
beta_mean = np.empty((self.dim, self.N))
for i in range(self.N):
history[:, :, i] = beta[i, :, :]
for j in range(self.dim):
beta_mean[j, :] = np.mean(history[:, j, :], axis=0)
history_all_h.append(history)
beta_mean_all_h.append(beta_mean)
history_all.append(history_all_h)
beta_mean_all.append(beta_mean_all_h)
return np.array(history_all), np.array(beta_mean_all)
|