def main():
### Set parameters ###
parameter_bounds = np.asarray( [[0,400]] )
training_size = 50
nugget = 1.e-10
n_clusters_max = 3
corr_kernel = 'exponential_periodic' # 'squared_exponential'
x_training = []
y_training = []
for i in range(training_size):
#x = np.random.uniform(parameter_bounds[0][0],parameter_bounds[0][1])
x = np.random.uniform(0,400)
x_training.append(x)
y_training.append(scoring_function(x))
x_training = np.atleast_2d(x_training).T
fig1 = plt.figure()
plt.title('Density estimation')
fig2 = plt.figure()
plt.title("GCP prediction")
n_rows = (n_clusters_max+1)/2
if not((n_clusters_max+1)% 2 == 0):
n_rows += 1
mf_plt_axis = np.asarray(range(100)) / 100.
mapping_functions_plot = []
for n_clusters in range(1,n_clusters_max+1):
gcp = GaussianCopulaProcess(nugget = nugget,
corr=corr_kernel,
random_start=5,
normalize = True,
coef_latent_mapping = 0.4,
n_clusters=n_clusters)
gcp.fit(x_training,y_training)
likelihood = gcp.reduced_likelihood_function_value_
print 'LGCP-'+str(n_clusters)+' fitted'
# print 'Theta', gcp.theta
print 'Likelihood',likelihood
if(n_clusters > 1):
centers = np.asarray([gcp.centroids[i][0]* gcp.X_std + gcp.X_mean for i in range(gcp.n_clusters) ], dtype=np.int32)
m = np.mean(y_training)
s = np.std(y_training)
y_mean, y_std = gcp.raw_y_mean,gcp.raw_y_std
x_density_plot = (np.asarray ( range(np.int(m *100.- 100.*(s)*10.),np.int(m*100. + 100.*(s)*10.)) ) / 100. - y_mean)/ y_std
ax1 = fig1.add_subplot(n_rows,2,n_clusters)
for i in range(gcp.n_clusters):
plt_density_gcp = gcp.density_functions[i](x_density_plot)
if(n_clusters > 1):
l = 'Cluster ' + str(centers[i])
else:
l = 'KDE estimation'
ax1.plot(x_density_plot*y_std + y_mean,plt_density_gcp,label=l)
ax1.legend()
ax1.set_title('n_clusters == ' + str(n_clusters) )
candidates = np.atleast_2d(range(80)).T * 5
prediction = gcp.predict(candidates)
# plot results
abs = range(0,400)
f_plot = [scoring_function(i) for i in abs]
ax2 = fig2.add_subplot(n_rows,2,n_clusters)
plt.plot(abs,f_plot)
plt.plot(x_training,y_training,'bo')
#plt.plot(candidates,simple_prediction,'go',label='Simple prediction')
plt.plot(candidates,prediction,'r+',label='n_clusters == ' + str(n_clusters))
plt.axis([0,400,0,1.])
ax2.set_title('Likelihood = ' + str(likelihood))
plt.legend()
mapping_functions_plot.append( [gcp.mapping(200,mf_plt_axis[i],normalize=True) for i in range(100)])
## with GP ##
gp = GaussianProcess(theta0=.1 ,
thetaL = 0.001,
thetaU = 10.,
random_start = 5,
nugget=nugget)
gp.fit(x_training,y_training)
likelihood = gp.reduced_likelihood_function_value_
print 'GP'
# print 'Theta',gp.theta_
print 'Likelihood',likelihood
candidates = np.atleast_2d(range(80)).T * 5
prediction = gp.predict(candidates)
# plot results
abs = range(0,400)
ax2 = fig2.add_subplot(n_rows,2,n_clusters_max+1)
plt.plot(abs,f_plot)
plt.plot(x_training,y_training,'bo')
plt.plot(candidates,prediction,'r+',label='GP')
plt.axis([0,400,0,1.])
ax2.set_title('Likelihood = ' + str(likelihood))
plt.legend()
ax1 = fig1.add_subplot(n_rows,2,n_clusters_max+1)
for i in range(n_clusters_max):
ax1.plot(mf_plt_axis,np.asarray(mapping_functions_plot[i])[:,0],label=str(i+1)+' clusters')
ax1.set_title('Mapping functions')
ax1.legend(loc=4)
plt.show()
def main():
save_plots = False
### Set parameters ###
nugget = 1.e-10
all_n_clusters = [1,2]
corr_kernel = 'exponential_periodic'
GCP_mapWithNoise= False
sampling_model = 'GCP'
integratedPrediction = False
coef_latent_mapping = 0.1
prediction_size = 1000
### Set parameters ###
parameter_bounds = np.asarray( [[0,400]] )
training_size = 40
if (save_plots):
if not os.path.exists('data_UCB'):
os.mkdir('data_UCB')
abs = np.atleast_2d(range(0,400)).T
f_plot = [scoring_function(i) for i in abs[:,0]]
x_training = []
y_training = []
for i in range(training_size):
x = np.random.uniform(0,400)
x_training.append(x)
y_training.append(scoring_function(x))
x_training = np.atleast_2d(x_training).T
candidates = []
real_y = []
for i in range(prediction_size):
x = [np.random.uniform(0,400)]
candidates.append(x)
real_y.append(scoring_function(x[0]))
real_y = np.asarray(real_y)
candidates = np.asarray(candidates)
count = -1
fig = plt.figure()
for n_clusters in all_n_clusters:
count += 2
ax = fig.add_subplot(len(all_n_clusters),2,count)
ax.set_title("GCP prediction")
gcp = GaussianCopulaProcess(nugget = nugget,
corr = corr_kernel,
random_start = 5,
n_clusters = n_clusters,
coef_latent_mapping = coef_latent_mapping,
mapWithNoise = GCP_mapWithNoise,
useAllNoisyY = False,
model_noise = None,
try_optimize = True)
gcp.fit(x_training,y_training)
print '\nGCP fitted'
print 'Likelihood', np.exp(gcp.reduced_likelihood_function_value_)
predictions,MSE,boundL,boundU = \
gcp.predict(candidates,
eval_MSE=True,
eval_confidence_bounds=True,
coef_bound = 1.96,
integratedPrediction=integratedPrediction)
pred_error = np.mean( (predictions - np.asarray(real_y) ) **2. )
print 'SMSE', pred_error / (np.std(real_y) **2.)
idx = np.argsort(candidates[:,0])
s_candidates = candidates[idx,0]
s_boundL = boundL[idx]
s_boundU = boundU[idx]
pred,MSE_bis = gcp.predict(np.atleast_2d(s_candidates).T,
eval_MSE=True,
transformY=False,
eval_confidence_bounds=False,
coef_bound = 1.96)
gp_boundL = pred - 1.96*np.sqrt(MSE_bis)
gp_boundU = pred + 1.96*np.sqrt(MSE_bis)
t_f_plot = [gcp.mapping(abs[i],f_plot[i],normalize=True) for i in range(len(f_plot))]
t_y_training = [gcp.mapping(x_training[i],y_training[i],normalize=True) for i in range(len(y_training))]
if(save_plots):
save_data = np.asarray([s_candidates,boundL,boundU,predictions,f_plot]).T
np.savetxt('data_UCB/data_plot.csv',save_data,delimiter=',')
ax.plot(abs,f_plot)
l1, = ax.plot(candidates,predictions,'r+',label='GCP predictions')
l3, = ax.plot(x_training,y_training,'bo',label='Training points')
ax.fill(np.concatenate([s_candidates,s_candidates[::-1]]),np.concatenate([s_boundL,s_boundU[::-1]]),alpha=.5, fc='c', ec='None')
ax = fig.add_subplot(len(all_n_clusters),2,count+1)
ax.set_title('GP space')
ax.plot(abs,t_f_plot)
ax.plot(s_candidates,pred,'r+',label='GCP predictions')
ax.plot(x_training,t_y_training,'bo',label='Training points')
ax.fill(np.concatenate([s_candidates,s_candidates[::-1]]),np.concatenate([gp_boundL,gp_boundU[::-1]]),alpha=.5, fc='c', ec='None')
if(save_plots):
t_save_data = np.asarray([s_candidates,gp_boundL,gp_boundU,pred,np.asarray(t_f_plot)[:,0]]).T
np.savetxt('data_UCB/gpspace_data_plot.csv',t_save_data,delimiter=',')
training_points = np.asarray([x_training[:,0],y_training,np.asarray(t_y_training)[:,0]]).T
np.savetxt('data_UCB/train_data_plot.csv',training_points,delimiter=',')
plt.legend()
plt.show()
def main():
save_plots = False
### Set parameters ###
nugget = 1.e-10
all_n_clusters = [1]
corr_kernel = 'squared_exponential'
GCP_mapWithNoise = False
sampling_model = 'GCP'
integratedPrediction = False
coef_latent_mapping = 0.1
prediction_size = 1000
### Set parameters ###
parameter_bounds = np.asarray([[0, 15], [0, 15]])
training_size = 50
x_training = []
y_training = []
for i in range(training_size):
x = [
np.random.uniform(parameter_bounds[j][0], parameter_bounds[j][1])
for j in range(parameter_bounds.shape[0])
]
x_training.append(x)
y_training.append(branin_f(x)[0])
x_training = np.asarray(x_training)
candidates = []
real_y = []
for i in range(prediction_size):
x = [
np.random.uniform(parameter_bounds[j][0], parameter_bounds[j][1])
for j in range(parameter_bounds.shape[0])
]
candidates.append(x)
real_y.append(branin_f(x)[0])
real_y = np.asarray(real_y)
candidates = np.asarray(candidates)
for n_clusters in all_n_clusters:
fig = plt.figure()
ax = fig.add_subplot(1, 2, 1, projection='3d')
ax.set_title("GCP prediction")
gcp = GaussianCopulaProcess(nugget=nugget,
corr=corr_kernel,
random_start=5,
n_clusters=n_clusters,
coef_latent_mapping=coef_latent_mapping,
mapWithNoise=GCP_mapWithNoise,
useAllNoisyY=False,
model_noise=None,
try_optimize=True)
gcp.fit(x_training, y_training)
print '\nGCP fitted'
print 'Likelihood', np.exp(gcp.reduced_likelihood_function_value_)
predictions,MSE,boundL,boundU = \
gcp.predict(candidates,eval_MSE=True,eval_confidence_bounds=True,coef_bound = 1.96,integratedPrediction=integratedPrediction)
pred_error = np.mean((predictions - np.asarray(real_y))**2.)
print 'MSE', pred_error
print 'Normalized error', np.sqrt(pred_error) / np.std(real_y)
pred, MSE_bis = gcp.predict(candidates,
eval_MSE=True,
transformY=False,
eval_confidence_bounds=False,
coef_bound=1.96)
t_f_plot = [
gcp.mapping(candidates[i], real_y[i], normalize=True)
for i in range(real_y.shape[0])
]
t_y_training = [
gcp.mapping(x_training[i], y_training[i], normalize=True)
for i in range(len(y_training))
]
ax.scatter(x_training[:, 0],
x_training[:, 1],
y_training,
c='g',
label='Training points',
alpha=0.5)
ax.scatter(candidates[:, 0],
candidates[:, 1],
real_y,
c='b',
label='Branin function',
alpha=0.5)
ax.scatter(candidates[:, 0],
candidates[:, 1],
predictions,
c='r',
label='predictions',
marker='+')
ax = fig.add_subplot(1, 2, 2, projection='3d')
ax.set_title('GP space')
ax.scatter(x_training[:, 0],
x_training[:, 1],
t_y_training,
c='g',
label='Training points',
alpha=0.5)
ax.scatter(candidates[:, 0],
candidates[:, 1],
t_f_plot,
c='b',
label='Branin function',
alpha=0.5)
ax.scatter(candidates[:, 0],
candidates[:, 1],
pred,
c='r',
label='predictions',
marker='+')
plt.legend()
plt.show()
def main():
save_plots = False
### Set parameters ###
nugget = 1.e-10
all_n_clusters = [1]
corr_kernel = 'squared_exponential'
GCP_mapWithNoise= False
sampling_model = 'GCP'
integratedPrediction = False
coef_latent_mapping = 0.1
prediction_size = 1000
### Set parameters ###
parameter_bounds = np.asarray( [[0,15],[0,15]] )
training_size = 50
x_training = []
y_training = []
for i in range(training_size):
x = [np.random.uniform(parameter_bounds[j][0],parameter_bounds[j][1]) for j in range(parameter_bounds.shape[0])]
x_training.append(x)
y_training.append(branin_f(x)[0])
x_training = np.asarray(x_training)
candidates = []
real_y = []
for i in range(prediction_size):
x = [np.random.uniform(parameter_bounds[j][0],parameter_bounds[j][1]) for j in range(parameter_bounds.shape[0])]
candidates.append(x)
real_y.append(branin_f(x)[0])
real_y = np.asarray(real_y)
candidates = np.asarray(candidates)
for n_clusters in all_n_clusters:
fig = plt.figure()
ax = fig.add_subplot(1,2,1, projection='3d')
ax.set_title("GCP prediction")
gcp = GaussianCopulaProcess(nugget = nugget,
corr = corr_kernel,
random_start = 5,
n_clusters = n_clusters,
coef_latent_mapping = coef_latent_mapping,
mapWithNoise = GCP_mapWithNoise,
useAllNoisyY = False,
model_noise = None,
try_optimize = True)
gcp.fit(x_training,y_training)
print '\nGCP fitted'
print 'Likelihood', np.exp(gcp.reduced_likelihood_function_value_)
predictions,MSE,boundL,boundU = \
gcp.predict(candidates,eval_MSE=True,eval_confidence_bounds=True,coef_bound = 1.96,integratedPrediction=integratedPrediction)
pred_error = np.mean( (predictions - np.asarray(real_y) ) **2. )
print 'MSE', pred_error
print 'Normalized error', np.sqrt(pred_error) /np.std(real_y)
pred,MSE_bis = gcp.predict(candidates,eval_MSE=True,transformY=False,eval_confidence_bounds=False,coef_bound = 1.96)
t_f_plot = [gcp.mapping(candidates[i],real_y[i],normalize=True) for i in range(real_y.shape[0])]
t_y_training = [gcp.mapping(x_training[i],y_training[i],normalize=True) for i in range(len(y_training))]
ax.scatter(x_training[:,0],x_training[:,1],y_training,c='g',label='Training points',alpha=0.5)
ax.scatter(candidates[:,0],candidates[:,1],real_y,c='b',label='Branin function',alpha=0.5)
ax.scatter(candidates[:,0],candidates[:,1],predictions,c='r',label='predictions',marker='+')
ax = fig.add_subplot(1,2,2, projection='3d')
ax.set_title('GP space')
ax.scatter(x_training[:,0],x_training[:,1],t_y_training,c='g',label='Training points',alpha=0.5)
ax.scatter(candidates[:,0],candidates[:,1],t_f_plot,c='b',label='Branin function',alpha=0.5)
ax.scatter(candidates[:,0],candidates[:,1],pred,c='r',label='predictions',marker='+')
plt.legend()
plt.show()
