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()