def run_case():
print('--> Load data set')
training_data = np.load('./datasets/basilisk_ASP_train.npy')
subset = np.arange(0, 1000, 1)
x_t = uc.cfix(training_data[subset, 0:2]) # training inputs
psi_t = uc.cfix(training_data[subset, 2]) # training outputs
n_data = np.alen(psi_t)
print('--> Load validation set')
validation_data = np.load('./datasets/basilisk_ASP_test.npy')
x_p = uc.cfix(validation_data[subset, 0:2]) # training inputs
psi_v = uc.cfix(validation_data[subset, 2]) # training outputs
print('--> Load prediction set')
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, 2)
x_p = x_p.reshape(n_pred, 2)
config = {
'xi': x_t,
'y': y_t,
}
ell2 = 1.00**2
s2 = 200.
per = 0.5
noise = 1.E-4
hyp = np.zeros([4, 1])
hyp[0] = ell2
hyp[1] = s2
hyp[2] = per
hyp[3] = noise
hyp = np.log(hyp.flatten())
ans = gp.learning_pe_iso(hyp, config)
print ans.message
hyp = np.exp(ans.x)
ell2 = hyp[0]
s2 = hyp[1]
per = hyp[2]
noise = hyp[3]
params = {'ell2': ell2, 's2': s2, 'per': per}
print('--> Initialising model variables')
t0 = time()
new_psi_p, var_psi_p = gp.predict_pe_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_psi_p)
holl_score = 0.
for ii in xrange(0, n_pred):
holl_score += uc.loglik_gp2circle(psi_v[ii], new_psi_p[ii], s2_p[ii])
print 'HOLL score: ' + str(holl_score)
print('Finished running case!')
def toy_fun(x):
return uc.cfix(15 * mexhat(0.9 * x, 0.15, 0.25) * x**2 + 0.75)
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('--> 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
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('--> Calculate kernel')
# Set kernel parameters
noise = 1.E-2
params = {
's2': 250.00,
'ell2': 5.50E-2**2,
}
k1 = np.array([[10.]])
k2 = np.array([[0.]])
y_t = y_t.reshape(n_data, 1)
x_t = x_t.reshape(n_data, 1)
x_p = x_p.reshape(grid_pts, 1)
x = np.vstack((x_p, x_t))
# Calculate kernels
mat_k_cc = kernels.se_iso(x, x, params)
mat_k_ss = kernels.se_iso(x, x, params)
mat_k = np.bmat([[mat_k_cc, np.zeros_like(mat_k_cc)],
[np.zeros_like(mat_k_ss), mat_k_ss]])
mat_k = np.asarray(mat_k)
mat_k += noise * np.eye(mat_k.shape[0])
# Find inverse
mat_ell = la.cholesky(mat_k, lower=True)
mat_kin = la.solve(mat_ell.T, la.solve(mat_ell, np.eye(mat_ell.shape[0])))
print('--> Initialising model variables')
psi_p = (2. * np.random.rand(n_pred, 1) - 1)
mf_k1 = np.log(np.random.rand(n_totp, 1) * 10)
mf_m1 = (2. * np.random.rand(n_totp, 1) - 1)
n_var = psi_p.shape[0] + mf_k1.shape[0] + mf_m1.shape[0]
idx = np.arange(0, n_var)
config = {
'N_data':
n_data,
'N_pred':
n_pred,
'c_data':
np.cos(y_t),
's_data':
np.sin(y_t),
'c_2data':
np.cos(2 * y_t),
's_2data':
np.sin(2 * y_t),
'Kinv':
mat_kin,
'idx_psi_p':
idx[0:psi_p.shape[0]],
'idx_mf_k1':
idx[psi_p.shape[0]:psi_p.shape[0] + mf_k1.shape[0]],
'idx_mf_m1':
idx[psi_p.shape[0] + mf_k1.shape[0]:psi_p.shape[0] + mf_k1.shape[0] +
mf_m1.shape[0]],
'k1':
k1,
'k2':
k2
}
xin = np.vstack((psi_p, mf_k1, mf_m1))
print('--> Starting optimisation')
t0 = time()
results = mgvm.vi.inference_model_opt(xin, config)
tf = time()
print 'Total elapsed time: ' + str(tf - t0) + ' s'
print results.message
# Keep all values between -pi and pi
new_psi_p = uc.cfix(results.x[config['idx_psi_p']])
new_mf_k1 = results.x[config['idx_mf_k1']]
new_mf_m1 = results.x[config['idx_mf_m1']]
# Predictions
print('--> Saving and displaying results')
# First the heatmap in the background
p, th = mgvm.vi.predictive_dist(n_pred,
new_mf_k1,
new_mf_m1,
k1,
0.,
pi_shift=True)
fig, scaling_x, scaling_y, offset_y = plot.circular_error_bars(th, p, True)
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 = uc.cfix(new_psi_p) * 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.) # training set
plot.plot(scaled_x_v, scaled_y_v, 'ob', fillstyle='none') # training set
plot.xticks([0, 20, 40, 60, 80, 100],
['0.0', '0.2', '0.4', '0.6', '0.8', '1.0'])
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 += uc.holl(y_v[ii], new_psi_p[ii], 0, k1, 0)
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('--> Load data set')
training_data = np.load('./datasets/basilisk_ASP_train.npy')
subset = np.arange(0, 1000, 1)
x_t = uc.cfix(training_data[subset, 0:2]) # training inputs
psi_t = uc.cfix(training_data[subset, 2]) # training outputs
n_data = np.alen(psi_t)
print('--> Load validation set')
validation_data = np.load('./datasets/basilisk_ASP_test.npy')
x_p = uc.cfix(validation_data[subset, 0:2]) # training inputs
psi_v = uc.cfix(validation_data[subset, 2]) # training outputs
print('--> Load prediction set')
n_pred = np.alen(x_p)
n_totp = n_data + n_pred
# Set kernel parameters
psi_t = psi_t.reshape(n_data, 1)
x_t = x_t.reshape(n_data, 2)
x_p = x_p.reshape(n_pred, 2)
print('--> Calculate kernel')
# Set kernel parameters
noise = 1E-4
params_cc = {'s2': 300.00, 'ell2': 2.5E-1**2, 'per': 6.0}
params_ss = params_cc
# params_cs = params_cc
k1 = np.array([[125.0]])
k2 = np.array([[0.0]])
x = np.vstack((x_p, x_t))
# Calculate kernels
mat_k_cc = kernels.pe_iso(x, x, params_cc)
mat_k_ss = kernels.pe_iso(x, x, params_ss)
mat_k_cs = np.zeros([n_totp, n_totp])
mat_k = np.bmat([[mat_k_cc, mat_k_cs], [mat_k_cs.T, mat_k_ss]])
mat_k = np.asarray(mat_k)
mat_k += noise * np.eye(mat_k.shape[0])
# Find inverse
mat_ell, jitter = ula.rchol(mat_k)
mat_kin = ula.invc(mat_ell)
print('--> Initialising model variables')
psi_p = (2 * np.random.rand(n_pred, 1) - 1) * 2
mf_k1 = np.log(np.random.rand(n_totp, 1) * 20.1)
mf_m1 = (2 * np.random.rand(n_totp, 1) - 1) * 2
n_var = psi_p.shape[0] + mf_k1.shape[0] + mf_m1.shape[0]
idx = np.arange(0, n_var)
config = {
'N_data':
n_data,
'N_pred':
n_pred,
'c_data':
np.cos(psi_t),
's_data':
np.sin(psi_t),
'c_2data':
np.cos(2 * psi_t),
's_2data':
np.sin(2 * psi_t),
'Kinv':
mat_kin,
'idx_psi_p':
idx[0:psi_p.shape[0]],
'idx_mf_k1':
idx[psi_p.shape[0]:psi_p.shape[0] + mf_k1.shape[0]],
'idx_mf_m1':
idx[psi_p.shape[0] + mf_k1.shape[0]:psi_p.shape[0] + mf_k1.shape[0] +
mf_m1.shape[0]],
'k1':
k1,
'k2':
k2,
}
xin = np.vstack((psi_p, mf_k1, mf_m1))
print('--> Starting optimisation')
t0 = time()
results = mgvm.vi.inference_model_opt(xin, config)
tf = time()
print 'Total elapsed time: ' + str(tf - t0) + ' s'
print results.message
# Predictions
print('--> Saving and displaying results')
holl_score = 0.
new_psi_p = uc.cfix(results.x[config['idx_psi_p']])
for ii in xrange(0, n_pred):
m1_idx = new_psi_p[ii]
m2_idx = new_psi_p[ii]
holl_score += uc.holl(psi_v[ii], m1_idx, m2_idx, k1, k2)
print 'HOLL score: ' + str(holl_score)
print('Finished running case!')
def run_case():
print('--> Load training set')
x_t = sio.loadmat('../datasets/compact_uber.mat')['x_t'] # training inputs
y_t = sio.loadmat(
'../datasets/compact_uber.mat')['y_t'] - np.pi # training outputs
n_data = np.alen(y_t)
print('--> Load validation set')
x_v = sio.loadmat('../datasets/compact_uber.mat')[
'x_v'] # validation inputs
y_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('--> Calculate kernel')
# Set kernel parameters
noise = 1E-1
params = {
's2': 250.00,
'ell2': 5.0E+1**2,
}
k1 = np.array([[4.0]])
k2 = np.array([[7.0]]) # previously 7.0
y_t = y_t.reshape(n_data, 1)
x_t = x_t.reshape(n_data, 1)
x_p = x_p.reshape(n_pred, 1)
x = np.vstack((x_p, x_t))
# Calculate kernels
mat_k_cc = kernels.se_iso(x, x, params)
mat_k_ss = kernels.se_iso(x, x, params)
mat_k = np.bmat([[mat_k_cc, np.zeros_like(mat_k_cc)],
[np.zeros_like(mat_k_ss), mat_k_ss]])
mat_k = np.asarray(mat_k)
mat_k += noise * np.eye(mat_k.shape[0])
# Find inverse
mat_ell = la.cholesky(mat_k, lower=True)
mat_kin = la.solve(mat_ell.T, la.solve(mat_ell, np.eye(mat_ell.shape[0])))
print('--> Initialising model variables')
psi_p = (2 * np.random.rand(n_pred, 1) - 1) * 2
mf_k1 = np.log(np.random.rand(n_totp, 1) * 0.1)
mf_m1 = (2 * np.random.rand(n_totp, 1) - 1) * 2
n_var = psi_p.shape[0] + mf_k1.shape[0] + mf_m1.shape[0]
idx = np.arange(0, n_var)
config = {
'N_data':
n_data,
'N_pred':
n_pred,
'c_data':
np.cos(y_t),
's_data':
np.sin(y_t),
'c_2data':
np.cos(2 * y_t),
's_2data':
np.sin(2 * y_t),
'Kinv':
mat_kin,
'idx_psi_p':
idx[0:psi_p.shape[0]],
'idx_mf_k1':
idx[psi_p.shape[0]:psi_p.shape[0] + mf_k1.shape[0]],
'idx_mf_m1':
idx[psi_p.shape[0] + mf_k1.shape[0]:psi_p.shape[0] + mf_k1.shape[0] +
mf_m1.shape[0]],
'k1':
k1,
'k2':
k2,
}
xin = np.vstack((psi_p, mf_k1, mf_m1))
print('--> Starting optimisation')
t0 = time()
results = mgvm.vi.inference_model_opt(xin, config)
tf = time()
print 'Total elapsed time: ' + str(tf - t0) + ' s'
print results.message
# Keep all values between -pi and pi
new_psi_p = uc.cfix(results.x[config['idx_psi_p']])
# Predictions
print('--> Saving and displaying results')
holl_score = 0.
for ii in xrange(0, n_pred):
m1_idx = new_psi_p[ii]
m2_idx = new_psi_p[ii]
holl_score += uc.holl(y_v[ii], m1_idx, m2_idx, k1, k2)
print 'HOLL score: ' + str(holl_score)
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!')
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_totp = n_data + n_pred
# Set kernel parameters
y_t = psi_t.reshape(n_data, 1)
x_t = x_t.reshape(n_data, d_input)
x_p = x_p.reshape(n_pred, d_input)
n_pred = np.alen(x_p)
n_totp = n_data + n_pred
print('--> Calculate kernel')
# Set kernel parameters
noise = 1E-1
params = {
's2': 250.00,
'ell2': 5.0E+1 ** 2,
}
k1 = np.array([[4.0]])
k2 = np.array([[7.0]]) # previously 7.0
x = np.vstack((x_p, x_t))
# Calculate kernels
mat_k_cc = kernels.se_iso(x, x, params)
mat_k_ss = kernels.se_iso(x, x, params)
mat_k = np.bmat([[mat_k_cc, np.zeros_like(mat_k_cc)], [np.zeros_like(mat_k_ss), mat_k_ss]])
mat_k = np.asarray(mat_k)
mat_k += noise * np.eye(mat_k.shape[0])
# Find inverse
mat_ell = la.cholesky(mat_k, lower=True)
mat_kin = la.solve(mat_ell.T, la.solve(mat_ell, np.eye(mat_ell.shape[0])))
print('--> Initialising model variables')
psi_p = (2 * np.random.rand(n_pred, 1) - 1) * 2
mf_k1 = np.log(np.random.rand(n_totp, 1) * 0.1)
mf_m1 = (2 * np.random.rand(n_totp, 1) - 1) * 2
n_var = psi_p.shape[0] + mf_k1.shape[0] + mf_m1.shape[0]
idx = np.arange(0, n_var)
config = {
'N_data': n_data,
'N_pred': n_pred,
'c_data': np.cos(y_t),
's_data': np.sin(y_t),
'c_2data': np.cos(2 * y_t),
's_2data': np.sin(2 * y_t),
'Kinv': mat_kin,
'idx_psi_p': idx[0:psi_p.shape[0]],
'idx_mf_k1': idx[psi_p.shape[0]:psi_p.shape[0] + mf_k1.shape[0]],
'idx_mf_m1': idx[psi_p.shape[0] + mf_k1.shape[0]:psi_p.shape[0] + mf_k1.shape[0] + mf_m1.shape[0]],
'k1': k1,
'k2': k2,
}
xin = np.vstack((psi_p, mf_k1, mf_m1))
print('--> Starting optimisation')
t0 = time()
results = mgvm.vi.inference_model_opt(xin, config)
tf = time()
print 'Total elapsed time: ' + str(tf - t0) + ' s'
# Keep all values between -pi and pi
new_psi_p = uc.cfix(results.x[config['idx_psi_p']])
# Predictions
print('--> Saving and displaying results')
holl_score = 0.
for ii in xrange(0, n_pred):
holl_score += uc.holl(psi_v[ii], new_psi_p[ii], 0, k1, k2)
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('--> Calcualte kernel')
# Set kernel parameters
params_cc = {
's2': 50.00,
'ell2': 5.0E-1**2,
}
params_ss = params_cc
y_t = y_t.reshape(n_data, 1)
x_t = x_t.reshape(n_data, 2)
x_p = x_p.reshape(n_pred, 2)
x = np.vstack((x_p, x_t))
# Calculate kernels
mat_k_cc = kernels.se_iso(x, x, params_cc)
mat_k_ss = kernels.se_iso(x, x, params_ss)
mat_k = np.bmat([[mat_k_cc, np.zeros_like(mat_k_cc)],
[np.zeros_like(mat_k_ss), mat_k_ss]])
mat_k = np.asarray(mat_k)
mat_k = mat_k + 1E-3 * np.eye(mat_k.shape[0])
# Find inverse
mat_ell = la.cholesky(mat_k, lower=True)
mat_kin = la.solve(mat_ell.T, la.solve(mat_ell, np.eye(mat_ell.shape[0])))
print('--> Initialising model variables')
psi_p = np.random.rand(n_pred, 1)
psi_p[0:np.floor(n_pred / 2)] *= (3 * np.pi / 4)
psi_p[np.floor(n_pred / 2):] *= 0.5
mf_k1 = np.log(np.random.rand(n_totp, 1) * 20)
mf_m1 = np.random.rand(n_totp, 1) * (-np.pi / 2)
k1 = np.array([[1.0]])
k2 = np.array([[10.]])
n_var = psi_p.shape[0] + mf_k1.shape[0] + mf_m1.shape[0]
idx = np.arange(0, n_var)
config = {
'N_data':
n_data,
'N_pred':
n_pred,
'c_data':
np.cos(y_t),
's_data':
np.sin(y_t),
'c_2data':
np.cos(2. * y_t),
's_2data':
np.sin(2. * y_t),
'Kinv':
mat_kin,
'idx_psi_p':
idx[0:psi_p.shape[0]],
'idx_mf_k1':
idx[psi_p.shape[0]:psi_p.shape[0] + mf_k1.shape[0]],
'idx_mf_m1':
idx[psi_p.shape[0] + mf_k1.shape[0]:psi_p.shape[0] + mf_k1.shape[0] +
mf_m1.shape[0]],
'k1':
k1,
'k2':
k2,
}
xin = np.vstack((psi_p, mf_k1, mf_m1))
print('--> Starting optimisation')
t0 = time()
results = mgvm.vi.inference_model_opt(xin, config)
tf = time()
print 'Total elapsed time: ' + str(tf - t0) + ' s'
print results.message
# Keep all values between -pi and pi
new_psi_p = uc.cfix(results.x[config['idx_psi_p']])
new_mf_k1 = results.x[config['idx_mf_k1']]
new_mf_m1 = results.x[config['idx_mf_m1']]
# Predictions
print('--> Saving and displaying results')
# First the heatmap in the background
p, th = mgvm.vi.predictive_dist(n_pred,
new_mf_k1,
new_mf_m1,
k1,
k2,
res=1000)
fig = plot.tides(th, p, y_t, y_v, pid_t, pid_v)
print('--> Calculating scores')
holl_score = 0.
train_ports = pid_t.flatten()
valid_ports = pid_v.flatten()
for ii in xrange(0, n_pred):
p_idx = p[:, ii]
m1_idx = new_psi_p[ii]
m2_idx = new_psi_p[ii]
if ii in train_ports:
y_t_idx = y_t[train_ports == ii]
else:
y_t_idx = y_v[valid_ports == ii]
holl_score += uc.holl(y_t_idx, m1_idx, m2_idx, k1, k2,
np.alen(y_t_idx))
print 'HOLL score: ' + str(holl_score)
print('Finished running case!')