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 / (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_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)
mapWithNoise = GCP_mapWithNoise,
useAllNoisyY = False,
model_noise = model_noise ,
try_optimize = True)
gcp.fit(x_training,y_training,y_detailed,obs_noise=noise_obs)
print 'GCP fitted'
print 'Theta', gcp.theta
predictions,MSE,boundL,boundU = \
gcp.predict(abs,eval_MSE=True,eval_confidence_bounds=True,coef_bound = 1.96)
pred,MSE_bis = gcp.predict(abs,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))]
t_all_y_training = [gcp.mapping(all_x[i],array_y_detailed[i],normalize=True) for i in range(array_y_detailed.shape[0])]
print pred.shape
idx = np.argsort(abs[:,0])
s_candidates = abs[idx,0]
s_boundL = boundL[idx]
s_boundU = boundU[idx]
if(save_plots):
save_data = np.asarray([s_candidates,boundL,boundU,predictions,f_plot]).T
np.savetxt('noisy_data_plot.csv',save_data,delimiter=',')
ax.plot(abs,f_plot)
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],
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)
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)
print 'GCP fitted'
print 'Theta', gcp.theta
predictions,MSE,boundL,boundU = \
gcp.predict(abs,eval_MSE=True,eval_confidence_bounds=True,coef_bound = 1.96)
pred, MSE_bis = gcp.predict(abs,
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))
]
t_all_y_training = [
gcp.mapping(all_x[i], array_y_detailed[i], normalize=True)
for i in range(array_y_detailed.shape[0])
]
print pred.shape
idx = np.argsort(abs[:, 0])
s_candidates = abs[idx, 0]
s_boundL = boundL[idx]
try_optimize = True)
gcp.fit(x_training,y_training)
print '\nGCP fitted'
print 'Theta', gcp.theta
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()
print 'MSE', 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_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')
