def run_test(training_size,
prediction_size,
function_name,
corr_kernel,
n_cluster,
prior='GCP'):
scoring_function = functions[function_name]
parameter_bounds = all_parameter_bounds[function_name]
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(scoring_function(x)[0])
if (isInt):
x_training, y_training = compute_unique2(
np.asarray(x_training, dtype=np.int32), np.asarray(y_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(scoring_function(x)[0])
real_y = np.asarray(real_y)
if (isInt):
candidates = np.asarray(candidates, dtype=np.int32)
if (prior == 'GP'):
gp = GaussianProcess(theta0=.1 * np.ones(parameter_bounds.shape[0]),
thetaL=0.001 * np.ones(parameter_bounds.shape[0]),
thetaU=10. * np.ones(parameter_bounds.shape[0]),
random_start=5,
nugget=nugget)
gp.fit(x_training, y_training)
pred = gp.predict(candidates)
likelihood = gp.reduced_likelihood_function_value_
else:
gcp = GaussianCopulaProcess(nugget=nugget,
corr=corr_kernel,
random_start=5,
normalize=True,
coef_latent_mapping=coef_latent_mapping,
n_clusters=n_clusters)
gcp.fit(x_training, y_training)
likelihood = gcp.reduced_likelihood_function_value_
if not (integratedPrediction):
pred = gcp.predict(candidates)
else:
pred, _, _, _ = gcp.predict(candidates,
eval_MSE=True,
eval_confidence_bounds=True,
integratedPrediction=True)
mse = np.mean((pred - real_y)**2.)
# Normalize
mse = mse / (np.std(real_y)**2.)
likelihood = np.exp(likelihood)
return [mse, likelihood]
def find_best_candidate_with_GCP(X,
raw_Y,
mean_Y,
std_Y,
args,
rand_candidates,
verbose,
acquisition_function='Simple'):
corr_kernel = args[0]
n_clusters = args[1]
GCP_mapWithNoise = args[2]
GCP_useAllNoisyY = args[3]
GCP_model_noise = args[4]
nugget = args[5]
GCP_upperBound_coef = args[6]
mean_gcp = GaussianCopulaProcess(nugget=nugget,
corr=corr_kernel,
random_start=5,
n_clusters=n_clusters,
mapWithNoise=GCP_mapWithNoise,
useAllNoisyY=GCP_useAllNoisyY,
model_noise=GCP_model_noise,
try_optimize=True)
mean_gcp.fit(X, mean_Y, raw_Y, obs_noise=std_Y)
if (verbose == 2):
print('GCP theta :' + str(mean_gcp.theta))
if (acquisition_function == 'Simple'):
predictions = mean_gcp.predict(rand_candidates,
eval_MSE=False,
eval_confidence_bounds=False)
best_candidate_idx = np.argmax(predictions)
best_candidate = rand_candidates[best_candidate_idx]
if (verbose == 2):
print 'Hopefully :', best_candidate, predictions[
best_candidate_idx]
elif (acquisition_function == 'UCB'):
predictions,MSE,boundL,boundU = \
mean_gcp.predict(rand_candidates,eval_MSE=True,eval_confidence_bounds=True,coef_bound = GCP_upperBound_coef)
best_candidate_idx = np.argmax(boundU)
best_candidate = rand_candidates[best_candidate_idx]
if (verbose == 2):
print 'Hopefully :', best_candidate, predictions[
best_candidate_idx], boundU[best_candidate_idx]
elif (acquisition_function == 'MaxLowerBound'):
predictions,MSE,boundL,boundU = \
mean_gcp.predict(rand_candidates,eval_MSE=True,eval_confidence_bounds=True,coef_bound = GCP_upperBound_coef)
best_candidate_idx = np.argmax(boundL)
best_candidate = rand_candidates[best_candidate_idx]
if (verbose == 2):
print 'Hopefully :', best_candidate, predictions[
best_candidate_idx], boundL[best_candidate_idx], boundU[
best_candidate_idx]
elif (acquisition_function == 'EI'):
predictions,MSE = \
mean_gcp.predict(rand_candidates,eval_MSE=True,transformY=False) # we want the predictions in the GP space
y_best = np.max(mean_Y)
sigma = np.sqrt(MSE)
ei = [ gcp_compute_ei((rand_candidates[i]-mean_gcp.X_mean)/mean_gcp.X_std,predictions[i],sigma[i],y_best, \
mean_gcp.mapping,mean_gcp.mapping_derivative) \
for i in range(rand_candidates.shape[0]) ]
best_candidate_idx = np.argmax(ei)
best_candidate = rand_candidates[best_candidate_idx]
if (verbose == 2):
print 'Hopefully :', best_candidate, predictions[
best_candidate_idx], ei[best_candidate_idx]
else:
print('Acquisition function not handled...')
return best_candidate
n_clusters=1,
coef_latent_mapping = 0.1,
try_optimize=True)
gcp.fit(params,m_o,output,obs_noise=std_o)
gp = GaussianProcess(theta0= 0.1 ,
thetaL = 0.001,
random_start=1,
thetaU = 10.,
nugget=1e-10)
gp.fit(params,m_o)
gp_pred,sigma = gp.predict(rand_candidates,eval_MSE=True)
gp_bu = np.asarray(gp_pred) + 1.96*np.sqrt(sigma)
print gp.theta_
predictions,mse,bl,bu = gcp.predict(rand_candidates,eval_MSE=True,eval_confidence_bounds=True,integratedPrediction= False,coef_bound=.5)
params_bis = (10*params[:,3] + 5* params[:,0] + params[:,1]) / 10.
params_bis2 = params[:,2] + (3.* params[:,4] / 10. )
cand_bis = (10*rand_candidates[:,3] + 5* rand_candidates[:,0] + rand_candidates[:,1]) / 10.
cand_bis2 = rand_candidates[:,2] + (3.* rand_candidates[:,4] / 10. )
fig = plt.figure()
ax = fig.add_subplot(1,1,1, projection='3d')
Z_min = np.min(m_o)
ax.scatter(params_bis2,params_bis,\
m_o, c=-np.exp((m_o-Z_min)**5.),cmap=cm.hot,marker='o')
ax.plot(cand_bis2,cand_bis,predictions,'b+')
ax.plot(cand_bis2,cand_bis,gp_pred,'g+')
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 '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])
]
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 '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 / (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))]
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 ##
gcp = GaussianCopulaProcess(nugget = nugget, corr = corr_kernel, random_start = 5, n_clusters = n_clusters, 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]
gcp = GaussianCopulaProcess(nugget=nugget,
corr=corr_kernel,
random_start=5,
n_clusters=n_clusters,
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))
(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()
mean_gcp = GaussianCopulaProcess(nugget=nugget,
corr=corr_kernel,
random_start=5,
n_clusters=n_clusters,
mapWithNoise=GCP_mapWithNoise,
useAllNoisyY=GCP_useAllNoisyY,
model_noise=GCP_model_noise,
try_optimize=True)
mean_gcp.fit(parameters,
mean_outputs,
raw_outputs,
obs_noise=std_outputs)
if (acquisition_function == 'UCB'):
predictions,MSE,boundL,boundU = \
mean_gcp.predict(rand_candidates,eval_MSE=True,eval_confidence_bounds=True,coef_bound = GCP_upperBound_coef)
best_candidate_idx = np.argmax(boundU)
best_candidate = rand_candidates[best_candidate_idx]
idx = np.argsort(rand_candidates[:, 0])
s_candidates = rand_candidates[idx, 0]
s_boundL = boundL[idx]
s_boundU = boundU[idx]
s_pred = predictions[idx]
ax = fig.add_subplot(n_rows, 3, i + 1)
ax.plot(abs, f_plot)
l1, = ax.plot(rand_candidates,
predictions,
'r+',
label='GCP predictions')
def run_test(training_size, prediction_size, function_name, corr_kernel, n_cluster, prior="GCP"):
scoring_function = functions[function_name]
parameter_bounds = all_parameter_bounds[function_name]
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(scoring_function(x)[0])
if isInt:
x_training, y_training = compute_unique2(np.asarray(x_training, dtype=np.int32), np.asarray(y_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(scoring_function(x)[0])
real_y = np.asarray(real_y)
if isInt:
candidates = np.asarray(candidates, dtype=np.int32)
if prior == "GP":
gp = GaussianProcess(
theta0=0.1 * np.ones(parameter_bounds.shape[0]),
thetaL=0.001 * np.ones(parameter_bounds.shape[0]),
thetaU=10.0 * np.ones(parameter_bounds.shape[0]),
random_start=5,
nugget=nugget,
)
gp.fit(x_training, y_training)
pred = gp.predict(candidates)
likelihood = gp.reduced_likelihood_function_value_
else:
gcp = GaussianCopulaProcess(
nugget=nugget,
corr=corr_kernel,
random_start=5,
normalize=True,
coef_latent_mapping=coef_latent_mapping,
n_clusters=n_clusters,
)
gcp.fit(x_training, y_training)
likelihood = gcp.reduced_likelihood_function_value_
if not (integratedPrediction):
pred = gcp.predict(candidates)
else:
pred, _, _, _ = gcp.predict(
candidates, eval_MSE=True, eval_confidence_bounds=True, integratedPrediction=True
)
mse = np.mean((pred - real_y) ** 2.0)
# Normalize
mse = mse / (np.std(real_y) ** 2.0)
likelihood = np.exp(likelihood)
return [mse, likelihood]
def find_best_candidate_with_GCP(X, raw_Y, mean_Y, std_Y, args, rand_candidates,verbose,acquisition_function='Simple'):
corr_kernel = args[0]
n_clusters = args[1]
GCP_mapWithNoise = args[2]
GCP_useAllNoisyY = args[3]
GCP_model_noise = args[4]
nugget = args[5]
GCP_upperBound_coef = args[6]
mean_gcp = GaussianCopulaProcess(nugget = nugget,
corr = corr_kernel,
random_start = 5,
n_clusters = n_clusters,
mapWithNoise = GCP_mapWithNoise,
useAllNoisyY = GCP_useAllNoisyY,
model_noise = GCP_model_noise,
try_optimize = True)
mean_gcp.fit(X,mean_Y,raw_Y,obs_noise=std_Y)
if(verbose == 2):
print ('GCP theta :'+str(mean_gcp.theta))
if(acquisition_function=='Simple'):
predictions = mean_gcp.predict(rand_candidates,eval_MSE=False,eval_confidence_bounds=False)
best_candidate_idx = np.argmax(predictions)
best_candidate = rand_candidates[best_candidate_idx]
if(verbose == 2):
print 'Hopefully :', best_candidate, predictions[best_candidate_idx]
elif(acquisition_function=='UCB'):
predictions,MSE,boundL,boundU = \
mean_gcp.predict(rand_candidates,eval_MSE=True,eval_confidence_bounds=True,coef_bound = GCP_upperBound_coef)
best_candidate_idx = np.argmax(boundU)
best_candidate = rand_candidates[best_candidate_idx]
if(verbose == 2):
print 'Hopefully :', best_candidate, predictions[best_candidate_idx], boundU[best_candidate_idx]
elif(acquisition_function=='MaxLowerBound'):
predictions,MSE,boundL,boundU = \
mean_gcp.predict(rand_candidates,eval_MSE=True,eval_confidence_bounds=True,coef_bound = GCP_upperBound_coef)
best_candidate_idx = np.argmax(boundL)
best_candidate = rand_candidates[best_candidate_idx]
if(verbose == 2):
print 'Hopefully :', best_candidate, predictions[best_candidate_idx], boundL[best_candidate_idx],boundU[best_candidate_idx]
elif(acquisition_function=='EI'):
predictions,MSE = \
mean_gcp.predict(rand_candidates,eval_MSE=True,transformY=False) # we want the predictions in the GP space
y_best = np.max(mean_Y)
sigma = np.sqrt(MSE)
ei = [ gcp_compute_ei((rand_candidates[i]-mean_gcp.X_mean)/mean_gcp.X_std,predictions[i],sigma[i],y_best, \
mean_gcp.mapping,mean_gcp.mapping_derivative) \
for i in range(rand_candidates.shape[0]) ]
best_candidate_idx = np.argmax(ei)
best_candidate = rand_candidates[best_candidate_idx]
if(verbose == 2):
print 'Hopefully :', best_candidate, predictions[best_candidate_idx], ei[best_candidate_idx]
else:
print('Acquisition function not handled...')
return best_candidate
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 'Theta', gcp.theta print 'Likelihood', np.exp(gcp.reduced_likelihood_function_value_) predictions = gcp.predict(candidates,eval_MSE=False,eval_confidence_bounds=False,coef_bound = 1.96,integratedPrediction=False) pred,mse = gcp.predict(candidates,eval_MSE=True,transformY=False) y_best =np.max(y_training) sigma = np.sqrt(mse) ei = [ utils.compute_ei((candidates[i]- gcp.X_mean) / gcp.X_std,pred[i],sigma[i],y_best, \ gcp.mapping,gcp.mapping_derivative) \ for i in range(candidates.shape[0]) ] ei = np.asarray(ei) print ei.shape for i in range(abs.shape[0]): f.write( str(candidates[i,0]) + ',' + str(f_plot[i]) +',' + str(predictions[i]) + ',' + str(ei[i]) +'\n' ) f.close() if(save_plots):
rand_candidates = utils.sample_candidates(n_candidates,parameter_bounds,isInt) if(sampling_model == 'GCP'): mean_gcp = GaussianCopulaProcess(nugget = nugget, corr = corr_kernel, random_start = 5, n_clusters = n_clusters, mapWithNoise = GCP_mapWithNoise, useAllNoisyY = GCP_useAllNoisyY, model_noise = GCP_model_noise, try_optimize = True) mean_gcp.fit(parameters,mean_outputs,raw_outputs,obs_noise=std_outputs) if(acquisition_function == 'UCB'): predictions,MSE,boundL,boundU = \ mean_gcp.predict(rand_candidates,eval_MSE=True,eval_confidence_bounds=True,coef_bound = GCP_upperBound_coef) best_candidate_idx = np.argmax(boundU) best_candidate = rand_candidates[best_candidate_idx] idx = np.argsort(rand_candidates[:,0]) s_candidates = rand_candidates[idx,0] s_boundL = boundL[idx] s_boundU = boundU[idx] s_pred = predictions[idx] ax = fig.add_subplot(n_rows,3,i+1) ax.plot(abs,f_plot) l1, = ax.plot(rand_candidates,predictions,'r+',label='GCP predictions') l2,= ax.plot(parameters,mean_outputs,'ro',label='GCP query points') l3, = ax.plot(X_init,Y_init,'bo',label='Random initialization') ax.fill(np.concatenate([s_candidates,s_candidates[::-1]]),np.concatenate([s_boundL,s_boundU[::-1]]),alpha=.5, fc='c', ec='None')
gcp.fit(x_training, y_training)
likelihood = gcp.reduced_likelihood_function_value_
print 'LGCP coef ' + str(coefs[j]) + ' 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(n_clusters)
],
dtype=np.int32)
candidates = np.atleast_2d(range(80)).T * 5
#simple_prediction = gcp.predict(candidates,integratedPrediction=False)
prediction = gcp.predict(candidates,
integratedPrediction=integratedPrediction)
abs = range(0, 400)
# plot mapping function
ax1 = fig1.add_subplot(n_rows, 2, j + 1)
for x in candidates[:, 0]:
ax1.plot(mf_plt_axis, [
gcp.mapping(x, mf_plt_axis[i], normalize=True)[0]
for i in range(100)
])
ax1.set_title('coef ' + str(coefs[j]))
# plot results
f_plot = [scoring_function(i) for i in abs]
ax2 = fig2.add_subplot(n_rows, 2, j + 1)
plt.plot(abs, f_plot)
random_start=5,
normalize = True,
coef_latent_mapping = coefs[j],
n_clusters=n_clusters)
gcp.fit(x_training,y_training)
likelihood = gcp.reduced_likelihood_function_value_
print 'LGCP coef '+str(coefs[j])+' 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(n_clusters) ], dtype=np.int32)
candidates = np.atleast_2d(range(80)).T * 5
#simple_prediction = gcp.predict(candidates,integratedPrediction=False)
prediction = gcp.predict(candidates,integratedPrediction=integratedPrediction)
abs = range(0,400)
# plot mapping function
ax1 = fig1.add_subplot(n_rows,2,j+1)
for x in candidates[:,0]:
ax1.plot(mf_plt_axis,[gcp.mapping(x,mf_plt_axis[i],normalize=True)[0] for i in range(100)])
ax1.set_title('coef ' + str(coefs[j]) )
# plot results
f_plot = [scoring_function(i) for i in abs]
ax2 = fig2.add_subplot(n_rows,2,j+1)
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))