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)])
##----------------------------------------------------------##
## STANDARD GP (prediction) ##
##----------------------------------------------------------##
xs = np.arange(2004+1./24.,2024-1./24.,1./12.) # TEST POINTS
xs = xs.reshape(len(xs),1)
vargout = gp(hyp,inffunc,meanfunc,covfunc,likfunc,x,y,xs)
ym = vargout[0]; ys2 = vargout[1]
m = vargout[2]; s2 = vargout[3]
plotter(xs,ym,ys2,x,y)#,[1955, 2030, 310, 420])
##----------------------------------------------------------##
## STANDARD GP (training) ##
## OPTIMIZE HYPERPARAMETERS ##
##----------------------------------------------------------##
## -> parameter training using (off the shelf) conjugent gradient (CG) optimization (NOTE: SCG is faster)
from time import clock
t0 = clock()
vargout = min_wrapper(hyp,gp,'SCG',inffunc,meanfunc,covfunc,likfunc,x,y,None,None,True)
t1 = clock()
hyp = vargout[0]
vargout = gp(hyp,inffunc,meanfunc,covfunc,likfunc,x,y,xs)
## SPECIFY inference method
inffunc = ['inferences.infLaplace']
## SET (hyper)parameters
hyp = hyperParameters()
hyp.mean = np.array([0.])
hyp.cov = np.array([0.,0.,0.])
[hyp_opt, fopt, gopt, funcCalls] = min_wrapper(hyp,gp,'Minimize',inffunc,meanfunc,covfunc,likfunc,x,y,None,None,True)
hyp = hyp_opt
##----------------------------------------------------------##
## STANDARD GP (example 1) ##
##----------------------------------------------------------##
print '...example 1: prediction...'
## GET negative log marginal likelihood
[nlml,dnlZ,post] = gp(hyp, inffunc, meanfunc, covfunc, likfunc, x, y, None, None, True)
print "nlml = ", nlml
## PREDICTION
[ymu,ys2,fmu,fs2,lp,post] = gp(hyp, inffunc, meanfunc, covfunc, likfunc, x, y, xstar, np.ones((n,1)) )
## PLOT log predictive probabilities
if PLOT:
fig = plt.figure()
plt.plot(x1[:,0], x1[:,1], 'b+', markersize = 12)
plt.plot(x2[:,0], x2[:,1], 'r+', markersize = 12)
pc = plt.contour(t1, t2, np.reshape(np.exp(lp), (t1.shape[0],t1.shape[1]) ))
fig.colorbar(pc)
plt.grid()
plt.axis([-4, 4, -4, 4])
plt.show()
## 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
## PLOT results
if PLOT:
plotter(xstar,ym,s2,x,y,[-2, 2, -0.9, 3.9])
## GET negative log marginal likelihood
[nlml, post] = gp(hyp,inffunc,meanfunc,covfunc,likfunc,x,y,None,None,False)
print "nlml =", nlml
##----------------------------------------------------------##
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
##----------------------------------------------------------##
## STANDARD GP (prediction) ##
##----------------------------------------------------------##
vargout = gp(hyp, inffunc, meanfunc, covfunc, likfunc, x, y, xs)
ym = vargout[0]
ys2 = vargout[1]
m = vargout[2]
s2 = vargout[3]
HousingPlotter(range(len(y)), y, range(len(y),
len(y) + len(ys)), ym, ys2,
range(len(y),
len(y) + len(ys)), ys)
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
##----------------------------------------------------------##
## STANDARD GP (prediction) ##
##----------------------------------------------------------##
vargout = gp(hyp,inffunc,meanfunc,covfunc,likfunc,x,y,xs)
ym = vargout[0]; ys2 = vargout[1]
m = vargout[2]; s2 = vargout[3]
HousingPlotter(range(len(y)),y,range(len(y),len(y)+len(ys)),ym,ys2,range(len(y),len(y)+len(ys)),ys)
##----------------------------------------------------------##
## STANDARD GP (training) ##
## OPTIMIZE HYPERPARAMETERS ##
##----------------------------------------------------------##
## -> parameter training using (off the shelf) conjugent gradient (CG) optimization (NOTE: SCG is faster)
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)])
##----------------------------------------------------------##
## STANDARD GP (prediction) ##
##----------------------------------------------------------##
xs = np.arange(2004 + 1. / 24., 2024 - 1. / 24., 1. / 12.) # TEST POINTS
xs = xs.reshape(len(xs), 1)
vargout = gp(hyp, inffunc, meanfunc, covfunc, likfunc, x, y, xs)
ym = vargout[0]
ys2 = vargout[1]
m = vargout[2]
s2 = vargout[3]
plotter(xs, ym, ys2, x, y) #,[1955, 2030, 310, 420])
##----------------------------------------------------------##
## STANDARD GP (training) ##
## OPTIMIZE HYPERPARAMETERS ##
##----------------------------------------------------------##
## -> parameter training using (off the shelf) conjugent gradient (CG) optimization (NOTE: SCG is faster)
from time import clock
t0 = clock()
vargout = min_wrapper(hyp, gp, 'SCG', inffunc, meanfunc, covfunc, likfunc,
x, y, None, None, True)
t1 = clock()
## SET (hyper)parameters
hyp = hyperParameters()
hyp.mean = np.array([0.])
hyp.cov = np.array([0., 0., 0.])
[hyp_opt, fopt, gopt,
funcCalls] = min_wrapper(hyp, gp, 'Minimize', inffunc, meanfunc, covfunc,
likfunc, x, y, None, None, True)
hyp = hyp_opt
##----------------------------------------------------------##
## STANDARD GP (example 1) ##
##----------------------------------------------------------##
print '...example 1: prediction...'
## GET negative log marginal likelihood
[nlml, dnlZ, post] = gp(hyp, inffunc, meanfunc, covfunc, likfunc, x, y,
None, None, True)
print "nlml = ", nlml
## PREDICTION
[ymu, ys2, fmu, fs2, lp, post] = gp(hyp, inffunc, meanfunc, covfunc,
likfunc, x, y, xstar, np.ones((n, 1)))
## PLOT log predictive probabilities
if PLOT:
fig = plt.figure()
plt.plot(x1[:, 0], x1[:, 1], 'b+', markersize=12)
plt.plot(x2[:, 0], x2[:, 1], 'r+', markersize=12)
pc = plt.contour(t1, t2,
np.reshape(np.exp(lp), (t1.shape[0], t1.shape[1])))
fig.colorbar(pc)
plt.grid()
## 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
## PLOT results
if PLOT:
plotter(xstar, ym, s2, x, y, [-2, 2, -0.9, 3.9])
## GET negative log marginal likelihood
[nlml, post] = gp(hyp, inffunc, meanfunc, covfunc, likfunc, x, y, None,
None, False)