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coregionalisation

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This commit is contained in:
James Hensman 2013-03-06 13:15:15 +00:00
parent f2ce47d96e
commit 613aae6417
4 changed files with 159 additions and 1 deletions
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69
GPy/examples/regression.py
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@ -75,6 +75,74 @@ def silhouette():
print(m)
return m
def coregionalisation_toy2():
"""
A simple demonstration of coregionalisation on two sinusoidal functions
"""
X1 = np.random.rand(50,1)*8
X2 = np.random.rand(30,1)*5
index = np.vstack((np.zeros_like(X1),np.ones_like(X2)))
X = np.hstack((np.vstack((X1,X2)),index))
Y1 = np.sin(X1) + np.random.randn(*X1.shape)*0.05
Y2 = np.sin(X2) + np.random.randn(*X2.shape)*0.05 + 2.
Y = np.vstack((Y1,Y2))
k1 = GPy.kern.rbf(1) + GPy.kern.bias(1)
k2 = GPy.kern.coregionalise(2,1)
k = k1.prod_orthogonal(k2)
m = GPy.models.GP_regression(X,Y,kernel=k)
m.constrain_fixed('rbf_var',1.)
m.constrain_positive('kappa')
m.ensure_default_constraints()
m.optimize()
pb.figure()
Xtest1 = np.hstack((np.linspace(0,9,100)[:,None],np.zeros((100,1))))
Xtest2 = np.hstack((np.linspace(0,9,100)[:,None],np.ones((100,1))))
mean, var,low,up = m.predict(Xtest1)
GPy.util.plot.gpplot(Xtest1[:,0],mean,low,up)
mean, var,low,up = m.predict(Xtest2)
GPy.util.plot.gpplot(Xtest2[:,0],mean,low,up)
pb.plot(X1[:,0],Y1[:,0],'rx',mew=2)
pb.plot(X2[:,0],Y2[:,0],'gx',mew=2)
return m
def coregionalisation_toy():
"""
A simple demonstration of coregionalisation on two sinusoidal functions
"""
X1 = np.random.rand(50,1)*8
X2 = np.random.rand(30,1)*5
index = np.vstack((np.zeros_like(X1),np.ones_like(X2)))
X = np.hstack((np.vstack((X1,X2)),index))
Y1 = np.sin(X1) + np.random.randn(*X1.shape)*0.05
Y2 = -np.sin(X2) + np.random.randn(*X2.shape)*0.05
Y = np.vstack((Y1,Y2))
k1 = GPy.kern.rbf(1)
k2 = GPy.kern.coregionalise(2,1)
k = k1.prod_orthogonal(k2)
m = GPy.models.GP_regression(X,Y,kernel=k)
m.constrain_fixed('rbf_var',1.)
m.constrain_positive('kappa')
m.ensure_default_constraints()
m.optimize()
pb.figure()
Xtest1 = np.hstack((np.linspace(0,9,100)[:,None],np.zeros((100,1))))
Xtest2 = np.hstack((np.linspace(0,9,100)[:,None],np.ones((100,1))))
mean, var,low,up = m.predict(Xtest1)
GPy.util.plot.gpplot(Xtest1[:,0],mean,low,up)
mean, var,low,up = m.predict(Xtest2)
GPy.util.plot.gpplot(Xtest2[:,0],mean,low,up)
pb.plot(X1[:,0],Y1[:,0],'rx',mew=2)
pb.plot(X2[:,0],Y2[:,0],'gx',mew=2)
return m
def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000):
"""Show an example of a multimodal error surface for Gaussian process regression. Gene 939 has bimodal behaviour where the noisey mode is higher."""
@ -160,3 +228,4 @@ def contour_data(data, length_scales, log_SNRs, signal_kernel_call=GPy.kern.rbf)
length_scale_lls.append(model.log_likelihood())
lls.append(length_scale_lls)
return np.array(lls)