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merged regression example, corrected refactoring
This commit is contained in:
Max Zwiessele
commit
802d6e7792
3 changed files with 68 additions and 54 deletions
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@ -25,7 +25,7 @@ def toy_rbf_1d(max_nb_eval_optim=100):
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print(m)
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return m
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def rogers_girolami_olympics(max_nb_eval_optim=100):
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def rogers_girolami_olympics(optim_iters=100):
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"""Run a standard Gaussian process regression on the Rogers and Girolami olympics data."""
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data = GPy.util.datasets.rogers_girolami_olympics()
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@ -37,14 +37,14 @@ def rogers_girolami_olympics(max_nb_eval_optim=100):
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# optimize
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m.ensure_default_constraints()
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m.optimize(max_f_eval=max_nb_eval_optim)
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m.optimize(max_f_eval=optim_iters)
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# plot
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m.plot(plot_limits = (1850, 2050))
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print(m)
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return m
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def toy_rbf_1d_50(max_nb_eval_optim=100):
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def toy_rbf_1d_50(optim_iters=100):
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"""Run a simple demonstration of a standard Gaussian process fitting it to data sampled from an RBF covariance."""
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data = GPy.util.datasets.toy_rbf_1d_50()
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@ -53,14 +53,14 @@ def toy_rbf_1d_50(max_nb_eval_optim=100):
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# optimize
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m.ensure_default_constraints()
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m.optimize(max_f_eval=max_nb_eval_optim)
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m.optimize(max_f_eval=optim_iters)
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# plot
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m.plot()
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print(m)
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return m
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def silhouette(max_nb_eval_optim=100):
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def silhouette(optim_iters=100):
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"""Predict the pose of a figure given a silhouette. This is a task from Agarwal and Triggs 2004 ICML paper."""
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data = GPy.util.datasets.silhouette()
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@ -69,12 +69,12 @@ def silhouette(max_nb_eval_optim=100):
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# optimize
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m.ensure_default_constraints()
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m.optimize(messages=True,max_f_eval=max_nb_eval_optim)
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m.optimize(messages=True,max_f_eval=optim_iters)
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print(m)
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return m
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def coregionalisation_toy2(max_nb_eval_optim=100):
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def coregionalisation_toy2(optim_iters=100):
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"""
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A simple demonstration of coregionalisation on two sinusoidal functions.
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"""
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@ -93,7 +93,7 @@ def coregionalisation_toy2(max_nb_eval_optim=100):
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m.constrain_fixed('.*rbf_var',1.)
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#m.constrain_positive('.*kappa')
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m.ensure_default_constraints()
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m.optimize('sim',messages=1,max_f_eval=max_nb_eval_optim)
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m.optimize('sim',messages=1,max_f_eval=optim_iters)
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pb.figure()
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Xtest1 = np.hstack((np.linspace(0,9,100)[:,None],np.zeros((100,1))))
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@ -106,7 +106,7 @@ def coregionalisation_toy2(max_nb_eval_optim=100):
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pb.plot(X2[:,0],Y2[:,0],'gx',mew=2)
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return m
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def coregionalisation_toy(max_nb_eval_optim=100):
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def coregionalisation_toy(optim_iters=100):
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"""
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A simple demonstration of coregionalisation on two sinusoidal functions.
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"""
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@ -125,7 +125,7 @@ def coregionalisation_toy(max_nb_eval_optim=100):
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m.constrain_fixed('.*rbf_var',1.)
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#m.constrain_positive('kappa')
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m.ensure_default_constraints()
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m.optimize(max_f_eval=max_nb_eval_optim)
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m.optimize(max_f_eval=optim_iters)
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pb.figure()
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Xtest1 = np.hstack((np.linspace(0,9,100)[:,None],np.zeros((100,1))))
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@ -139,7 +139,7 @@ def coregionalisation_toy(max_nb_eval_optim=100):
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return m
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def coregionalisation_sparse(max_nb_eval_optim=100):
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def coregionalisation_sparse(optim_iters=100):
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"""
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A simple demonstration of coregionalisation on two sinusoidal functions using sparse approximations.
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"""
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@ -164,7 +164,7 @@ def coregionalisation_sparse(max_nb_eval_optim=100):
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#m.constrain_positive('kappa')
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m.constrain_fixed('iip')
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m.ensure_default_constraints()
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m.optimize_restarts(5, robust=True, messages=1, max_f_eval=max_nb_eval_optim)
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m.optimize_restarts(5, robust=True, messages=1, max_f_eval=optim_iters)
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pb.figure()
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Xtest1 = np.hstack((np.linspace(0,9,100)[:,None],np.zeros((100,1))))
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@ -181,7 +181,7 @@ def coregionalisation_sparse(max_nb_eval_optim=100):
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return m
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def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000, max_nb_eval_optim=100):
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def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000, optim_iters=300):
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"""Show an example of a multimodal error surface for Gaussian process regression. Gene 939 has bimodal behaviour where the noisey mode is higher."""
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# Contour over a range of length scales and signal/noise ratios.
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@ -197,7 +197,7 @@ def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000
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data['Y'] = data['Y'] - np.mean(data['Y'])
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lls = GPy.examples.regression._contour_data(data, length_scales, log_SNRs, GPy.kern.rbf)
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pb.contour(length_scales, log_SNRs, np.exp(lls), 20)
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pb.contour(length_scales, log_SNRs, np.exp(lls), 20, cmap=pb.cm.jet)
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ax = pb.gca()
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pb.xlabel('length scale')
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pb.ylabel('log_10 SNR')
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@ -211,18 +211,20 @@ def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000
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optim_point_y = np.empty(2)
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np.random.seed(seed=seed)
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for i in range(0, model_restarts):
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kern = GPy.kern.rbf(1, variance=np.random.exponential(1.), lengthscale=np.random.exponential(50.)) + GPy.kern.white(1,variance=np.random.exponential(1.))
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#kern = GPy.kern.rbf(1, variance=np.random.exponential(1.), lengthscale=np.random.exponential(50.))
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kern = GPy.kern.rbf(1, variance=np.random.uniform(1e-3,1), lengthscale=np.random.uniform(5,50))
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m = GPy.models.GPRegression(data['X'],data['Y'], kernel=kern)
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optim_point_x[0] = m.get('rbf_lengthscale')
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optim_point_y[0] = np.log10(m.get('rbf_variance')) - np.log10(m.get('white_variance'));
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m['noise_variance'] = np.random.uniform(1e-3,1)
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optim_point_x[0] = m['rbf_lengthscale']
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optim_point_y[0] = np.log10(m['rbf_variance']) - np.log10(m['noise_variance']);
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# optimize
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m.ensure_default_constraints()
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m.optimize(xtol=1e-6, ftol=1e-6, max_f_eval=max_nb_eval_optim)
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m.optimize('scg', xtol=1e-6, ftol=1e-6, max_f_eval=optim_iters)
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optim_point_x[1] = m.get('rbf_lengthscale')
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optim_point_y[1] = np.log10(m.get('rbf_variance')) - np.log10(m.get('white_variance'));
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optim_point_x[1] = m['rbf_lengthscale']
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optim_point_y[1] = np.log10(m['rbf_variance']) - np.log10(m['noise_variance']);
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pb.arrow(optim_point_x[0], optim_point_y[0], optim_point_x[1]-optim_point_x[0], optim_point_y[1]-optim_point_y[0], label=str(i), head_length=1, head_width=0.5, fc='k', ec='k')
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models.append(m)
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@ -231,42 +233,35 @@ def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000
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ax.set_ylim(ylim)
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return (models, lls)
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def _contour_data(data, length_scales, log_SNRs, signal_kernel_call=GPy.kern.rbf):
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def _contour_data(data, length_scales, log_SNRs, kernel_call=GPy.kern.rbf):
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"""Evaluate the GP objective function for a given data set for a range of signal to noise ratios and a range of lengthscales.
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:data_set: A data set from the utils.datasets director.
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:length_scales: a list of length scales to explore for the contour plot.
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:log_SNRs: a list of base 10 logarithm signal to noise ratios to explore for the contour plot.
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:signal_kernel: a kernel to use for the 'signal' portion of the data."""
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:kernel: a kernel to use for the 'signal' portion of the data."""
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lls = []
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total_var = np.var(data['Y'])
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kernel = kernel_call(1, variance=1., lengthscale=1.)
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model = GPy.models.GPRegression(data['X'], data['Y'], kernel=kernel)
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for log_SNR in log_SNRs:
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SNR = 10**log_SNR
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SNR = 10.**log_SNR
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noise_var = total_var/(1.+SNR)
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signal_var = total_var - noise_var
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model.kern['.*variance'] = signal_var
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model['noise_variance'] = noise_var
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length_scale_lls = []
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for length_scale in length_scales:
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noise_var = 1.
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signal_var = SNR
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noise_var = noise_var/(noise_var + signal_var)*total_var
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signal_var = signal_var/(noise_var + signal_var)*total_var
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signal_kernel = signal_kernel_call(1, variance=signal_var, lengthscale=length_scale)
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noise_kernel = GPy.kern.white(1, variance=noise_var)
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kernel = signal_kernel + noise_kernel
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K = kernel.K(data['X'])
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total_var = (np.dot(np.dot(data['Y'].T,GPy.util.linalg.pdinv(K)[0]), data['Y'])/data['Y'].shape[0])[0,0]
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noise_var *= total_var
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signal_var *= total_var
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kernel = signal_kernel_call(1, variance=signal_var, lengthscale=length_scale) + GPy.kern.white(1, variance=noise_var)
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model = GPy.models.GPRegression(data['X'], data['Y'], kernel=kernel)
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model.constrain_positive('')
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model['.*lengthscale'] = length_scale
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length_scale_lls.append(model.log_likelihood())
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lls.append(length_scale_lls)
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return np.array(lls)
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def sparse_GP_regression_1D(N = 400, M = 5, max_nb_eval_optim=100):
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def sparse_GP_regression_1D(N = 400, M = 5, optim_iters=100):
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"""Run a 1D example of a sparse GP regression."""
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# sample inputs and outputs
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X = np.random.uniform(-3.,3.,(N,1))
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@ -281,11 +276,11 @@ def sparse_GP_regression_1D(N = 400, M = 5, max_nb_eval_optim=100):
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m.ensure_default_constraints()
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m.checkgrad(verbose=1)
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m.optimize('tnc', messages = 1, max_f_eval=max_nb_eval_optim)
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m.optimize('tnc', messages = 1, max_f_eval=optim_iters)
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m.plot()
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return m
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def sparse_GP_regression_2D(N = 400, M = 50, max_nb_eval_optim=100):
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def sparse_GP_regression_2D(N = 400, M = 50, optim_iters=100):
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"""Run a 2D example of a sparse GP regression."""
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X = np.random.uniform(-3.,3.,(N,2))
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Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(N,1)*0.05
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@ -306,12 +301,12 @@ def sparse_GP_regression_2D(N = 400, M = 50, max_nb_eval_optim=100):
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# optimize and plot
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pb.figure()
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m.optimize('tnc', messages = 1, max_f_eval=max_nb_eval_optim)
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m.optimize('tnc', messages = 1, max_f_eval=optim_iters)
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m.plot()
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print(m)
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return m
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def uncertain_inputs_sparse_regression(max_nb_eval_optim=100):
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def uncertain_inputs_sparse_regression(optim_iters=100):
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"""Run a 1D example of a sparse GP regression with uncertain inputs."""
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fig, axes = pb.subplots(1,2,figsize=(12,5))
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@ -327,7 +322,7 @@ def uncertain_inputs_sparse_regression(max_nb_eval_optim=100):
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# create simple GP model - no input uncertainty on this one
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m = GPy.models.SparseGPRegression(X, Y, kernel=k, Z=Z)
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m.ensure_default_constraints()
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m.optimize('scg', messages=1, max_f_eval=max_nb_eval_optim)
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m.optimize('scg', messages=1, max_f_eval=optim_iters)
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m.plot(ax=axes[0])
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axes[0].set_title('no input uncertainty')
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@ -335,7 +330,7 @@ def uncertain_inputs_sparse_regression(max_nb_eval_optim=100):
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#the same model with uncertainty
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m = GPy.models.SparseGPRegression(X, Y, kernel=k, Z=Z, X_variance=S)
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m.ensure_default_constraints()
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m.optimize('scg', messages=1, max_f_eval=max_nb_eval_optim)
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m.optimize('scg', messages=1, max_f_eval=optim_iters)
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m.plot(ax=axes[1])
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axes[1].set_title('with input uncertainty')
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print(m)
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