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plot_synthetic_data.py
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plot_synthetic_data.py
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import numpy as np
np.random.seed(123)
import matplotlib.pyplot as plt
d = 20
trainN = 2000
testN = 1000
M = 100
def gen_data(sigma, rho):
v = np.random.random((d,))
mean = np.zeros((d,))
cov = rho**2 * np.eye(d)
all_data = []
for m in range(M):
r_m = np.random.multivariate_normal(mean, cov)
u_m = v + r_m
x_m = np.random.uniform(-1.0, 1.0, (trainN+testN,d))
y_m = np.dot(x_m, u_m) + np.random.normal(0, sigma**2, (trainN+testN,))
train_x_m = x_m[:trainN]
train_y_m = y_m[:trainN]
test_x_m = x_m[trainN:]
test_y_m = y_m[trainN:]
#print (train_x_m)[:10]
#print (train_y_m)[:10]
#print (test_x_m)[:10]
#print (test_y_m)[:10]
#assert False
all_data.append((train_x_m, train_y_m, test_x_m, test_y_m))
return all_data
def local_model(all_data):
train_errors = []
test_errors = []
for (train_x_m, train_y_m, test_x_m, test_y_m) in all_data:
u_m_hat1 = np.linalg.inv(np.dot(np.transpose(train_x_m), train_x_m))
u_m_hat2 = np.dot(np.transpose(train_x_m), train_y_m)
u_m_hat = np.dot(u_m_hat1, u_m_hat2)
train_pred = np.dot(train_x_m, u_m_hat)
test_pred = np.dot(test_x_m, u_m_hat)
train_error = np.mean((train_pred - train_y_m)**2)
test_error = np.mean((test_pred - test_y_m)**2)
#print (train_pred)[:10]
#print (train_y_m)[:10]
#print (test_pred)[:10]
#print (test_y_m)[:10]
#assert False
train_errors.append(train_error)
test_errors.append(test_error)
return np.mean(train_errors), np.mean(test_errors)
def global_model(all_data):
all_train_x = []
all_train_y = []
all_test_x = []
all_test_y = []
for (train_x_m, train_y_m, test_x_m, test_y_m) in all_data:
all_train_x.append(train_x_m)
all_train_y.append(train_y_m)
all_test_x.append(test_x_m)
all_test_y.append(test_y_m)
all_train_x = np.concatenate(all_train_x, axis=0)
all_train_y = np.concatenate(all_train_y, axis=0)
all_test_x = np.concatenate(all_test_x, axis=0)
all_test_y = np.concatenate(all_test_y, axis=0)
v_hat1 = np.linalg.inv(np.dot(np.transpose(all_train_x), all_train_x))
v_hat2 = np.dot(np.transpose(all_train_x), all_train_y)
v_hat = np.dot(v_hat1, v_hat2)
train_pred = np.dot(all_train_x, v_hat)
test_pred = np.dot(all_test_x, v_hat)
train_error = np.mean((train_pred - all_train_y)**2)
test_error = np.mean((test_pred - all_test_y)**2)
return train_error, test_error
def local_global(all_data, alpha):
all_train_x = []
all_train_y = []
all_test_x = []
all_test_y = []
for (train_x_m, train_y_m, test_x_m, test_y_m) in all_data:
all_train_x.append(train_x_m)
all_train_y.append(train_y_m)
all_test_x.append(test_x_m)
all_test_y.append(test_y_m)
all_train_x = np.concatenate(all_train_x, axis=0)
all_train_y = np.concatenate(all_train_y, axis=0)
all_test_x = np.concatenate(all_test_x, axis=0)
all_test_y = np.concatenate(all_test_y, axis=0)
v_hat1 = np.linalg.inv(np.dot(np.transpose(all_train_x), all_train_x))
v_hat2 = np.dot(np.transpose(all_train_x), all_train_y)
v_hat = np.dot(v_hat1, v_hat2)
train_errors = []
test_errors = []
for (train_x_m, train_y_m, test_x_m, test_y_m) in all_data:
u_m_hat1 = np.linalg.inv(np.dot(np.transpose(train_x_m), train_x_m))
u_m_hat2 = np.dot(np.transpose(train_x_m), train_y_m)
u_m_hat = np.dot(u_m_hat1, u_m_hat2)
ensemble = alpha*u_m_hat + (1.0-alpha)*v_hat
train_pred = np.dot(train_x_m, ensemble)
test_pred = np.dot(test_x_m, ensemble)
train_error = np.mean((train_pred - train_y_m)**2)
test_error = np.mean((test_pred - test_y_m)**2)
train_errors.append(train_error)
test_errors.append(test_error)
return np.mean(train_errors), np.mean(test_errors)
# local better
# rho = 0.1
# sigma = 1.5
# plt.ylim(5.07, 5.14)
# local too good
# rho = 0.5
# sigma = 1.5
# plt.ylim(5.0, 8.0)
# global better
# rho = 0.06
# sigma = 1.5
# plt.ylim(5.06, 5.12)
# global too good
# rho = 0.02
# sigma = 1.5
# plt.ylim(5.04, 5.14)
sigmas = [i/10.0 for i in range(11)]
rhos = [i/10.0 for i in range(11)]
alphas = [i/10.0 for i in range(11)]
ls = []
gs = []
lgs = []
rho = 0.5
sigma = 1.5
all_data = gen_data(sigma, rho)
for alpha in alphas:
local_train_err, local_test_err = local_model(all_data)
global_train_err, global_test_err = global_model(all_data)
lg_train_err, lg_test_err = local_global(all_data, alpha)
ls.append(local_test_err)
gs.append(global_test_err)
lgs.append(lg_test_err)
fig, ax = plt.subplots()
# We change the fontsize of minor ticks label
ax.tick_params(axis='both', which='major', labelsize=20)
ax.tick_params(axis='both', which='minor', labelsize=20)
plt.plot(alphas, ls, label='Local only', linewidth=3.0)
plt.plot(alphas, gs, label='FedAvg', linewidth=3.0)
plt.plot(alphas,lgs, label='LG-FedAvg', linewidth=3.0)
plt.legend(fontsize=20)
#plt.xlabel('\alpha', fontsize=18)
plt.ylim(5.0, 8.0)
#plt.yticks([])
#plt.ylabel('average test error', fontsize=18)
plt.show()
assert False
#for sigma in sigmas:
#for rho in rhos:
for alpha in alphas:
rho = 0.5
sigma = 0.5
all_data = gen_data(sigma, rho)
local_train_err, local_test_err = local_model(all_data)
global_train_err, global_test_err = global_model(all_data)
# alpha1 = (M-1)/float(M) * rho**2 + float(d)/(M*trainN) * sigma**2
# alpha2 = (M-1)/float(M) * rho**2 + float((M+1)*d)/(M*trainN) * sigma**2
# alpha = alpha1 / float(alpha2)
print 'alpha', alpha
lg_train_err, lg_test_err = local_global(all_data, alpha)
print sigma, local_test_err, global_test_err, lg_test_err
ls.append(local_test_err)
gs.append(global_test_err)
lgs.append(lg_test_err)
#assert False
plt.plot(ls, label='l')
plt.plot(gs, label='g')
plt.plot(lgs, label='lg')
plt.legend()
plt.show()