n,D = x.shape
## DEFINE parameterized covariance function
P = D # The dimension of the input
N = 5
covfunc = [ ['kernels.covSum'], [[ ['kernels.covProd'], P*[[ ['kernels.covSum'], N*[['kernels.covSpectralSingle']] ]] ], ['kernels.covNoise'] ] ]
## DEFINE parameterized mean function
meanfunc = [ ['means.meanZero'] ]
## DEFINE parameterized inference and liklihood functions
inffunc = ['inferences.infExact']
likfunc = ['likelihoods.likGauss']
## SET (hyper)parameters
hyp = hyperParameters()
## SET (hyper)parameters for covariance and mean
hyp.cov = np.log(np.random.random(4*N*P+1))
# Now replace the values of hyp.cov that correspond to the indices for P
for ii in range(P):
for jj in range(N):
ind = ii*N*4 + jj*4 + 4
hyp.cov[ind-1] = ii
hyp.mean = np.array([])
sn = 0.1
hyp.lik = np.array([np.log(sn)])
##----------------------------------------------------------##
ys = np.reshape(data[-N:, -1], (N, 1))
ys = (ys - np.mean(ys)) / (np.std(ys) + 1.e-16)
N, D = x.shape
## DEFINE parameterized covariance function
covfunc = [['kernels.covSum'], [['kernels.covSEiso'],
['kernels.covNoise']]]
## DEFINE parameterized mean function
meanfunc = [['means.meanZero']]
## DEFINE parameterized inference and liklihood functions
inffunc = ['inferences.infExact']
likfunc = ['likelihoods.likGauss']
## SET (hyper)parameters
hyp = hyperParameters()
## SET (hyper)parameters for covariance and mean
hyp.cov = np.random.normal(0., 1., (3, ))
hyp.mean = np.array([])
hyp.lik = np.array([np.log(0.1)])
print 'Initial mean = ', hyp.mean
print 'Initial covariance = ', hyp.cov
print 'Initial liklihood = ', hyp.lik
[nlml, post] = gp(hyp, inffunc, meanfunc, covfunc, likfunc, x, y, None,
None, False)
print 'Initial negative log marginal likelihood = ', nlml
plt.axis([-1.9,1.9,-0.9,3.9])
plt.grid()
plt.xlabel('input x')
plt.ylabel('output y')
plt.show()
## DEFINE parameterized mean and covariance functions
covfunc = [['kernels.covMatern']]
meanfunc = [ ['means.meanSum'], [ ['means.meanLinear'] , ['means.meanConst'] ] ]
## DEFINE likelihood function used
likfunc = ['likelihoods.likGauss']
## SPECIFY inference method
inffunc = ['inferences.infExact']
## SET (hyper)parameters
hyp = hyperParameters()
hyp.cov = np.array([np.log(0.25),np.log(1.0),3.0])
hyp.mean = np.array([0.5,1.0])
hyp.lik = np.array([np.log(0.1)])
##----------------------------------------------------------##
## STANDARD GP (example 1) ##
##----------------------------------------------------------##
print '...example 1: prediction...'
## PREDICTION
t0 = clock()
vargout = gp(hyp,inffunc,meanfunc,covfunc,likfunc,x,y,xstar)
t1 = clock()
ym = vargout[0]; ys2 = vargout[1]; m = vargout[2]; s2 = vargout[3]
print 'Time for prediction =',t1-t0
plt.axis([-1.9, 1.9, -0.9, 3.9])
plt.grid()
plt.xlabel('input x')
plt.ylabel('output y')
plt.show()
## DEFINE parameterized mean and covariance functions
covfunc = [['kernels.covMatern']]
meanfunc = [['means.meanSum'], [['means.meanLinear'], ['means.meanConst']]]
## DEFINE likelihood function used
likfunc = ['likelihoods.likGauss']
## SPECIFY inference method
inffunc = ['inferences.infExact']
## SET (hyper)parameters
hyp = hyperParameters()
hyp.cov = np.array([np.log(0.25), np.log(1.0), 3.0])
hyp.mean = np.array([0.5, 1.0])
hyp.lik = np.array([np.log(0.1)])
##----------------------------------------------------------##
## STANDARD GP (example 1) ##
##----------------------------------------------------------##
print '...example 1: prediction...'
## PREDICTION
t0 = clock()
vargout = gp(hyp, inffunc, meanfunc, covfunc, likfunc, x, y, xstar)
t1 = clock()
ym = vargout[0]
ys2 = vargout[1]
m = vargout[2]