def run_case():
print('--> Load training set')
x_t = sio.loadmat('../datasets/compact_uber.mat')['x_t'] # training inputs
psi_t = sio.loadmat('../datasets/compact_uber.mat')['y_t'] - np.pi # training outputs
n_data = np.alen(psi_t)
print('--> Load validation set')
x_v = sio.loadmat('../datasets/compact_uber.mat')['x_v'] # validation inputs
psi_v = sio.loadmat('../datasets/compact_uber.mat')['y_v'] - np.pi # validation outputs
print('--> Load prediction set')
x_p = sio.loadmat('../datasets/compact_uber.mat')['x_p'] # prediction inputs
n_pred = np.alen(x_p)
n_totp = n_data + n_pred
print('--> Learn GP')
# Set kernel parameters
psi_t = psi_t.reshape(n_data, 1)
y_t = np.hstack((np.cos(psi_t), np.sin(psi_t)))
x_t = x_t.reshape(n_data, 1)
x_p = x_p.reshape(n_pred, 1)
config = {
'xi': x_t,
'y': y_t,
}
ell2 = 0.15 ** 2
s2 = 400.
noise = 1.E-6
hyp = np.zeros([3, 1])
hyp[0] = ell2
hyp[1] = s2
hyp[2] = noise
hyp = np.log(hyp.flatten())
ans = gp.learning_se_iso(hyp, config)
print ans.message
hyp = np.exp(ans.x)
ell2 = hyp[0]
s2 = hyp[1]
noise = hyp[2]
params = {
'ell2': ell2,
's2': s2
}
print('--> Initialising model variables')
t0 = time()
yp, var_yp = gp.predict_se_iso(y_t, x_t, x_p, params, noise)
tf = time()
print 'Total elapsed time in prediction: ' + str(tf - t0) + ' s'
# Keep all values between -pi and pi
s2_p = np.diag(var_yp)
holl_score = 0.
for ii in xrange(0, n_pred):
holl_score += uc.loglik_gp2circle(psi_v[ii, 0], yp[ii], s2_p[ii])
print 'HOLL score: ' + str(holl_score)
print('Finished running case!')
def run_case():
x = np.linspace(0, 1, 100)
y = toy_fun(x)
print('--> Create training set')
x_t = np.array([
+0.05, +0.05, +0.17, +0.17, +0.22, +0.30, +0.35, +0.37, +0.52, +0.53,
+0.69, +0.70, +0.82, +0.90
])
psi_t = np.array([
+0.56, +0.65, +0.90, +1.18, +2.39, +3.40, +2.89, +2.64, -2.69, -3.20,
-3.40, -2.77, +0.41, +0.35
])
x_v = x
psi_v = y
n_data = np.alen(x_t)
print('--> Create prediction set')
grid_pts = 100
x_p = np.linspace(0, 1, grid_pts)
n_pred = np.alen(x_p)
n_totp = n_data + n_pred
print('--> Learn GP')
# Set kernel parameters
psi_t = psi_t.reshape(n_data, 1)
y_t = np.hstack((np.cos(psi_t), np.sin(psi_t)))
x_t = x_t.reshape(n_data, 1)
x_p = x_p.reshape(n_pred, 1)
config = {
'xi': x_t,
'y': y_t,
}
ell2 = 1.15**2
s2 = 700.
noise = 2.E-3
hyp = np.zeros([3, 1])
hyp[0] = ell2
hyp[1] = s2
hyp[2] = noise
hyp = np.log(hyp.flatten())
ans = gp.learning_se_iso(hyp, config)
print ans.message
hyp = np.exp(ans.x)
ell2 = hyp[0]
s2 = hyp[1]
noise = hyp[2]
params = {'ell2': ell2, 's2': s2}
print('--> Initialising model variables')
t0 = time()
yp, var_yp = gp.predict_se_iso(y_t, x_t, x_p, params, noise)
tf = time()
print 'Total elapsed time in prediction: ' + str(tf - t0) + ' s'
# Keep all values between -pi and pi
z_p = yp[:, 0] + 1.j * yp[:, 1]
s2_p = np.diag(var_yp)
new_psi_p = np.angle(z_p)
n_grid = 1000
p, th = gp.get_predictive_for_wrapped(new_psi_p, var_yp, res=n_grid)
# Predictions
print('--> Saving and displaying results')
# First the heatmap in the background
fig, scaling_x, scaling_y, offset_y = plot.circular_error_bars(th, p, True)
# Then scale the predicted and training sets to match the dimensions of the heatmap
scaled_x_t = x_t * scaling_x
scaled_y_t = uc.cfix(psi_t) * scaling_y + offset_y
scaled_x_p = x_p * scaling_x
scaled_y_p = uc.cfix(new_psi_p) * scaling_y + offset_y
scaled_x_v = x_v * scaling_x
scaled_y_v = uc.cfix(psi_v) * scaling_y + offset_y
# Now plot the optimised psi's and datapoints
plot.plot(scaled_x_p, scaled_y_p, 'c.') # optimised prediction
plot.plot(scaled_x_t, scaled_y_t, 'xk', mew=2.0) # training set
plot.plot(scaled_x_v, scaled_y_v, 'ob', fillstyle='none') # held out set
plot.ylabel('Regressed variable $(\psi)$')
plot.xlabel('Input variable $(x)$')
plot.tight_layout()
plot.grid(True)
holl_score = 0.
for ii in xrange(0, n_pred):
holl_score += uc.loglik_gp2circle(psi_v[ii], yp[ii], s2_p[ii])
print 'HOLL score: ' + str(holl_score)
print('Finished running case!')
def run_case():
print('--> Load data set')
data = list()
with open('../datasets/Spellman-alpha.csv', 'rb') as csvfile:
reader = csv.reader(csvfile)
for row in reader:
data.append(row)
data = np.array(data[1:]).astype(np.float_)
train_idx = np.arange(0, 18, 2)
valid_idx = np.arange(1, 18, 2)
print('--> Preparing training set')
x_t = data[train_idx, 1:] # training inputs
psi_t = data[train_idx, 0] # training outputs
n_data = np.alen(psi_t)
d_input = x_t.shape[1]
print('--> Preparing validation set')
x_v = data[valid_idx, 1:] # validation inputs
psi_v = data[valid_idx, 0].reshape(len(valid_idx), 1) # validation outputs
print('--> Load prediction set')
x_p = x_v # prediction inputs
n_pred = x_p.shape[0]
n_pred = np.alen(x_p)
n_totp = n_data + n_pred
print('--> Learn GP')
# Set kernel parameters
psi_t = psi_t.reshape(n_data, 1)
y_t = np.hstack((np.cos(psi_t), np.sin(psi_t)))
x_t = x_t.reshape(n_data, d_input)
x_p = x_p.reshape(n_pred, d_input)
config = {
'xi': x_t,
'y': y_t,
}
ell2 = 0.15 ** 2
s2 = 400.
noise = 1.E-6
hyp = np.zeros([3, 1])
hyp[0] = ell2
hyp[1] = s2
hyp[2] = noise
hyp = np.log(hyp.flatten())
ans = gp.learning_se_iso(hyp, config)
print ans.message
hyp = np.exp(ans.x)
ell2 = hyp[0]
s2 = hyp[1]
noise = hyp[2]
params = {
'ell2': ell2,
's2': s2
}
print('--> Initialising model variables')
t0 = time()
yp, var_yp = gp.predict_se_iso(y_t, x_t, x_p, params, noise)
tf = time()
print 'Total elapsed time in prediction: ' + str(tf - t0) + ' s'
s2_p = np.diag(var_yp)
holl_score = 0.
for ii in xrange(0, n_pred):
holl_score += np.sum(-0.5 * (yp[ii] - psi_v[ii]) ** 2 / s2_p[ii] - 0.5 * np.log(s2_p[ii] * 2. * np.pi))
print 'HOLL score: ' + str(holl_score)
print('Finished running case!')
def run_case():
print('--> Load training set')
x_t = sio.loadmat('../datasets/simpletide.mat')['x_t'] # training inputs
y_t = sio.loadmat('../datasets/simpletide.mat')['y_t'] - np.pi # training outputs
pid_t = sio.loadmat('../datasets/simpletide.mat')['pid_t'] # port ids for training set
n_data = np.alen(y_t)
print('--> Load validation set')
x_v = sio.loadmat('../datasets/simpletide.mat')['x_v'] # validation inputs
y_v = sio.loadmat('../datasets/simpletide.mat')['y_v'] - np.pi # validation outputs
pid_v = sio.loadmat('../datasets/simpletide.mat')['pid_v'] # port ids for validation set
print('--> Load prediction set')
x_p = sio.loadmat('../datasets/simpletide.mat')['x_p'] # prediction inputs
pid_p = sio.loadmat('../datasets/simpletide.mat')['pid_p'] # port ids for prediction set
n_pred = np.alen(x_p)
n_totp = n_data + n_pred
print('--> Learn GP')
# Set kernel parameters
y_t = y_t.reshape(n_data, 1)
x_t = x_t.reshape(n_data, 2)
x_p = x_p.reshape(n_pred, 2)
config = {
'xi': x_t,
'y': y_t,
}
ell2 = 0.15 ** 2
s2 = 400.
noise = 1.E-6
hyp = np.zeros([3, 1])
hyp[0] = ell2
hyp[1] = s2
hyp[2] = noise
hyp = np.log(hyp.flatten())
ans = gp.learning_se_iso(hyp, config)
print ans.message
hyp = np.exp(ans.x)
ell2 = hyp[0]
s2 = hyp[1]
noise = hyp[2]
params = {
'ell2': ell2,
's2': s2
}
print('--> Initialising model variables')
t0 = time()
y_p, var_y_p = gp.predict_se_iso(y_t, x_t, x_p, params, noise)
tf = time()
s2_p = np.diag(var_y_p)
print 'Total elapsed time in prediction: ' + str(tf - t0) + ' s'
# Keep all values between -pi and pi
new_psi_p = uc.cfix(y_p)
print('--> Calculating scores')
holl_score = 0.
for ii in xrange(0, n_pred):
holl_score += np.sum(-0.5 * (new_psi_p[ii] - y_v[ii]) ** 2 / s2_p[ii] - 0.5 * np.log(s2_p[ii] * 2. * np.pi))
print 'HOLL score: ' + str(holl_score)
print('Finished running case!')
def run_case():
print('--> Create training set')
x = np.linspace(0, 1, 100)
y = toy_fun(x)
x_t = np.array([
+0.05, +0.05, +0.17, +0.17, +0.22, +0.30, +0.35, +0.37, +0.52, +0.53,
+0.69, +0.70, +0.82, +0.90
])
y_t = np.array([
+0.56, +0.65, +0.90, +1.18, +2.39, +3.40, +2.89, +2.64, -2.69, -3.20,
-3.40, -2.77, +0.41, +0.35
])
x_v = x
y_v = y
y_t = uc.cfix(y_t)
y_v = uc.cfix(y_v)
n_data = np.alen(x_t)
print('--> Create prediction set')
grid_pts = 100
x_p = np.linspace(0, 1, grid_pts)
n_pred = np.alen(x_p)
n_totp = n_data + n_pred
print('--> Learn GP')
# Set kernel parameters
y_t = y_t.reshape(n_data, 1)
x_t = x_t.reshape(n_data, 1)
x_p = x_p.reshape(n_pred, 1)
config = {
'xi': x_t,
'y': y_t,
}
ell2 = 0.5**2
s2 = 200.
noise = 1.E-4
hyp = np.zeros([3, 1])
hyp[0] = ell2
hyp[1] = s2
hyp[2] = noise
hyp = np.log(hyp.flatten())
ans = gp.learning_se_iso(hyp, config)
print ans.message
hyp = np.exp(ans.x)
ell2 = hyp[0]
s2 = hyp[1]
noise = hyp[2]
params = {'ell2': ell2, 's2': s2}
print('--> Initialising model variables')
t0 = time()
yp, var_yp = gp.predict_se_iso(y_t, x_t, x_p, params, noise)
tf = time()
print 'Total elapsed time in prediction: ' + str(tf - t0) + ' s'
new_psi_p = yp
s2_p = np.diag(var_yp)
p, th = gp.get_predictive_for_plots_1d(yp, var_yp, res=1000)
# Predictions
print('--> Saving and displaying results')
# First the heatmap in the background
fig, scaling_x, scaling_y, offset_y = plot.circular_error_bars(th, p, True)
# Then scale the predicted and training sets to match the dimensions of the heatmap
scaled_x_t = x_t * scaling_x
scaled_y_t = uc.cfix(y_t) * scaling_y + offset_y
scaled_x_v = x_v * scaling_x
scaled_y_v = uc.cfix(y_v) * scaling_y + offset_y
scaled_x_p = x_p * scaling_x
scaled_y_p = new_psi_p * scaling_y + offset_y
# scaled_mode = (mode + np.pi) * 1000 / (2 * np.pi)
# Now plot the optimised psi's and datapoints
plot.plot(scaled_x_p, scaled_y_p, 'c.') # optimised prediction
plot.plot(scaled_x_t, scaled_y_t, 'xk', mew=2.0) # training set
plot.plot(scaled_x_v, scaled_y_v, 'ob', fillstyle='none') # training set
plot.ylabel('Regressed variable $(\psi)$')
plot.xlabel('Input variable $(x)$')
plot.tight_layout()
holl_score = 0.
for ii in xrange(0, y_v.shape[0]):
holl_score += -np.sum(0.5 * (yp[ii] - y_v[ii])**2 / s2_p[ii] -
0.5 * np.log(s2_p[ii] * 2. * np.pi))
print 'HOLL Score: ' + str(holl_score)
print('Finished running case!')