# generate data set
xMin, xMax = -5, 5
np.random.seed(5)
Xc = np.ones([n, 1])
Xc[:, 0] = np.linspace(xMin, xMax, n)
Yc = 10 * np.sinc(Xc[:, 0]) + np.random.normal(0, 1, n)
X, x, Y, y = train_test_split(Xc, Yc, test_size=0.5, random_state=0)
# train rvr
rvr = RVR(gamma=1, kernel='rbf')
mem_us_rvr = memory_usage((rvr.fit, (X, Y)), interval=0.1)
print(mem_us_rvr)
t1 = time.time()
rvr.fit(X, Y)
t2 = time.time()
rvr_err = mean_squared_error(rvr.predict(x), y)
rvs = np.sum(rvr.active_)
print "RVR error on test set is {0}, number of relevant vectors is {1}, time {2}".format(
rvr_err, rvs, t2 - t1)
# train svr
svr = GridSearchCV(SVR(kernel='rbf', gamma=1),
param_grid={'C': [0.001, 0.1, 1, 10, 100]},
cv=10)
mem_us_svr = memory_usage((svr.fit, (X, Y)), interval=0.1)
t1 = time.time()
svr.fit(X, Y)
t2 = time.time()
from sklearn.metrics import mean_squared_error
# parameters
n = 5000
# generate data set
np.random.seed(0)
Xc = np.ones([n, 1])
Xc[:, 0] = np.linspace(-5, 5, n)
Yc = 10 * np.sinc(Xc[:, 0]) + np.random.normal(0, 1, n)
X, x, Y, y = train_test_split(Xc, Yc, test_size=0.5, random_state=0)
# train rvr
rvm = RVR(gamma=1, kernel='rbf')
t1 = time.time()
rvm.fit(X, Y)
t2 = time.time()
y_hat, var = rvm.predict_dist(x)
rvm_err = mean_squared_error(y_hat, y)
rvs = np.sum(rvm.active_)
print("RVM error on test set is {0}, number of relevant vectors is {1}, time {2}".format(rvm_err, rvs, t2 - t1))
# train svr
svr = GridSearchCV(SVR(kernel='rbf', gamma=1), param_grid={'C': [0.001, 0.1, 1, 10, 100]}, cv=10)
t1 = time.time()
svr.fit(X, Y)
t2 = time.time()
svm_err = mean_squared_error(svr.predict(x), y)
svs = svr.best_estimator_.support_vectors_.shape[0]
print(print()
)
y_lin = svr_lin.fit(x_val, y_val).predict(x_val)
t2 = time.time()
t_svr_lin = t2 - t1
print('Support Vector Regression with linear kernel takes {} s'.format(
t_svr_lin))
t1 = time.time()
y_poly = svr_poly.fit(x_val, y_val).predict(x_val)
t2 = time.time()
t_svr_poly = t2 - t1
print('Support Vector Regression with polynomial kernel takes {} s'.format(
t_svr_poly))
# Proceed reression using Relevance Vector Regression (RVR)
t1 = time.time()
y_rvr = rvm.fit(x_val, y_val).predict(x_val)
t2 = time.time()
t_rvr = t2 - t1
print('Relevance Vector Regression takes {} s'.format(t_rvr))
# Plot Data
plt.scatter(x_val, y_val, color='red', label='Datapoints')
plt.hold('on')
plt.xlim([x_min, x_max])
plt.plot(x2_val, [sin(x2_val[i]) for i in range(len(x2_val))],
c='k',
label='Original function')
# Regression Plot
lw = 2
plt.plot(x_val, y_rbf, color='navy', lw=lw, label='RBF model')
plt.plot(x_val, y_lin, color='c', lw=lw, label='Linear model')