def test_gp():
# Generate data
func = lambda x: np.sin(x*2*np.pi/5)
x = np.random.uniform(low=0, high=10, size=(100,))
f = func(x)
f = f + np.random.normal(0, 0.2, np.shape(f))
plt.clf()
plt.plot(x,f,'r+')
#plt.plot(x,y,'r+')
# Construct model
ls = EF.NodeConstantScalar(1.5, name='lengthscale')
amp = EF.NodeConstantScalar(2.0, name='amplitude')
noise = EF.NodeConstantScalar(0.6, name='noise')
K = CF.SquaredExponential(amp, ls)
K_noise = CF.Delta(noise)
K_sum = CF.Sum(K, K_noise)
M = GP.Constant(lambda x: (x/10-2)*(x/10+1))
method = 'multi'
if method == 'sum':
# Sum GP
F = GP.GaussianProcess(M, K_sum)
elif method == 'multi':
# Joint for latent function and observation process
M_multi = GP.Multiple([M, M])
K_zeros = CF.Zeros()
#K_multi = CF.Multiple([[K, K],[K,K_sum]])
K_multi1 = CF.Multiple([[K, K],[K,K]])
#K_multi2 = CF.Multiple([[None, None],[None, K_noise]])
K_multi2 = CF.Multiple([[K_zeros, K_zeros],[K_zeros,K_noise]])
xp = np.arange(0,5,1)
F = GP.GaussianProcess(M_multi, K_multi1,
k_sparse=K_multi2,
#pseudoinputs=[[],xp])
pseudoinputs=None)
#F = GP.GaussianProcess(M_multi, K_multi, pseudoinputs=[[],xp])
# Observations are from the latter process:
#xf = np.array([])
#x_pseudo = [[], x]
#x_full = [np.array([15, 20]), []]
#xy = x
#x = [xf, xy]
#f = np.concatenate([func(xf), f])
#f_pseudo = f
#f_full = func(x_full)
x = [[], x]
# Inference
#F.observe(x_pseudo, f_pseudo, pseudo=True)
F.observe(x, f)
utils.vb_optimize_nodes(ls, amp, noise)
F.update()
u = F.get_parameters()
print('parameters')
print(ls.name)
print(ls.u[0])
print(amp.name)
print(amp.u[0])
print(noise.name)
print(noise.u[0])
#print(F.lower_bound_contribution())
# Posterior predictions
xh = np.arange(-5, 20, 0.1)
if method == 'multi':
# Choose which process you want to examine:
(fh, varfh) = u([[],xh], covariance=1)
#(fh, varfh) = u([xh,[]], covariance=1)
else:
(fh, varfh) = u(xh, covariance=1)
#print(fh)
#print(np.shape(fh))
#print(np.shape(varfh))
varfh[varfh<0] = 0
errfh = np.sqrt(varfh)
#print(varfh)
#print(errfh)
m_errorplot(xh, fh, errfh, errfh)
return
# Construct a GP
k = gp_cov_se(magnitude=theta1, lengthscale=theta2)
f = NodeGP(0, k)
f.observe(x, y)
f.update()
(mp, kp) = f.get_parameters()
def test_sparse_gp():
## Generate data
# Noisy observations from a sinusoid
N = 10000
func = lambda x: np.sin(x*2*np.pi/20)
x = np.random.uniform(low=0, high=N, size=(N,))
f = func(x)
y = f + np.random.normal(0, 0.2, np.shape(f))
# Plot data
plt.clf()
plt.plot(x,y,'r+')
## Construct model
# Covariance function stuff
ls = EF.NodeConstantScalar(3, name='lengthscale')
amp = EF.NodeConstantScalar(2.0, name='amplitude')
noise = EF.NodeConstantScalar(0.6, name='noise')
# Latent process covariance
#K_f = CF.SquaredExponential(amp, ls)
K_f = CF.PiecewisePolynomial2(amp, ls)
# Noise process covariance
K_noise = CF.Delta(noise)
# Observation process covariance
K_y = CF.Sum(K_f, K_noise)
# Joint covariance
#K_joint = CF.Multiple([[K_f, K_f],[K_f,K_y]], sparse=True)
# Mean function stuff
M = GP.Constant(lambda x: (x/10-2)*(x/10+1))
# Means for latent and observation processes
#M_multi = GP.Multiple([M, M])
# Gaussian process
F = GP.GaussianProcess(M, [[K_f, K_f], [K_f, K_y]])
#F = GP.GaussianProcess(M, [[K_f, K_f], [K_f, K_y]])
#F = GP.GaussianProcess(M_multi, K_joint)
## Inference
F.observe([[],x], y)
utils.vb_optimize_nodes(ls, amp, noise)
F.update()
u = F.get_parameters()
## Show results
# Print hyperparameters
print('parameters')
print(ls.name, ls.u[0])
print(amp.name, amp.u[0])
print(noise.name, noise.u[0])
# Posterior predictions
xh = np.arange(np.min(x)-5, np.max(x)+10, 0.1)
(fh, varfh) = u([[],xh], covariance=1)
#(fh, varfh) = u([xh,[]], covariance=1)
# Plot predictive distribution
varfh[varfh<0] = 0
errfh = np.sqrt(varfh)
m_errorplot(xh, fh, errfh, errfh)
return