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))