merged local branch

GPy/examples/warped_GP_demo.py

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-# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
-# Licensed under the BSD 3-clause license (see LICENSE.txt)
-
-
-import numpy as np
-import scipy as sp
-import pdb, sys, pickle
-import matplotlib.pylab as plt
-import GPy
-np.random.seed(2)
-
-N = 120
-# sample inputs and outputs
-X = np.random.uniform(-np.pi,np.pi,(N,1))
-Y = np.sin(X)+np.random.randn(N,1)*0.05
-Y += np.abs(Y.min()) + 0.5
-Z = np.exp(Y)#Y**(1/3.0)
-Zmax = Z.max()
-Zmin = Z.min()
-Z = (Z-Zmin)/(Zmax-Zmin) - 0.5
-train = range(X.shape[0])[:100]
-test = range(X.shape[0])[100:]
-
-kernel = GPy.kern.rbf(1) + GPy.kern.bias(1)
-m = GPy.models.warpedGP(X[train], Z[train], kernel=kernel, warping_terms = 2)
-m.constrain_positive('(tanh_a|tanh_b|rbf|noise|bias)')
-m.constrain_fixed('tanh_d', 1.0)
-m.randomize()
-plt.figure()
-plt.xlabel('predicted f(Z)')
-plt.ylabel('actual f(Z)')
-plt.plot(m.likelihood.Y, Y[train], 'o', alpha = 0.5, label = 'before training')
-m.optimize(messages = True)
-# m.optimize_restarts(4, parallel = True, messages = True)
-plt.plot(m.likelihood.Y, Y[train], 'o', alpha = 0.5, label = 'after training')
-plt.legend(loc = 0)
-m.plot_warping()
-plt.figure()
-plt.title('warped GP fit')
-m.plot()
-m.optimize(messages=1)
-plt.figure(); plt.plot(m.predict(X[test])[0].flatten(), Y[test].flatten(), 'x'); plt.title('prediction in unwarped space')
-m.predict_in_warped_space = True
-plt.figure(); plt.plot(m.predict(X[test])[0].flatten(), Z[test].flatten(), 'x'); plt.title('prediction in warped space')
-
-m1 = GPy.models.GP_regression(X[train], Z[train])
-m1.constrain_positive('(rbf|noise|bias)')
-m1.randomize()
-m1.optimize(messages = True)
-plt.figure()
-plt.title('GP fit')
-m1.plot()