##----------------------------------------------------------##
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)
ym = vargout[0]; ys2 = vargout[1]
m = vargout[2]; s2 = vargout[3]
print 'Time to optimize = ',t1-t0
print 'Optimized mean = ',hyp.mean
print 'Optimized covariance = ',hyp.cov
print 'Optimized liklihood = ',hyp.lik
plotter(xs,ym,ys2,x,y,[1955, 2030, 310, 420])
if PLOT:
plotter(xstar,ym,ys2,x,y,[-2, 2, -0.9, 3.9])
## GET negative log marginal likelihood
[nlml, post] = gp(hyp2,inffunc,meanfunc,covfunc,likfunc,x,y,None,None,False)
print "nlml =", nlml
##----------------------------------------------------------##
## STANDARD GP (example 3) ##
##----------------------------------------------------------##
print '...example 3: training and prediction...'
## TRAINING: OPTIMIZE HYPERPARAMETERS
## -> parameter training via off-the-shelf optimization
t0 = clock()
[hyp2_opt, fopt, gopt, funcCalls] = min_wrapper(hyp2,gp,'Minimize',inffunc,meanfunc,covfunc,likfunc,x,y,None,None,True) # minimize
#[hyp2_opt, fopt, gopt, funcCalls] = min_wrapper(hyp2,gp,'CG',inffunc,meanfunc,covfunc,likfunc,x,y,None,None,True) # conjugent gradient
#[hyp2_opt, fopt, gopt, funcCalls] = min_wrapper(hyp2,gp,'SCG',inffunc,meanfunc,covfunc,likfunc,x,y,None,None,True) # scaled conjugent gradient (faster than CG)
#[hyp2_opt, fopt, gopt, funcCalls] = min_wrapper(hyp2,gp,'BFGS',inffunc,meanfunc,covfunc,likfunc,x,y,None,None,True) # quasi-Newton method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS)
t1 = clock()
print 'Time for optimization =',t1-t0
print "Optimal nlml =", fopt
## PREDICTION
vargout = gp(hyp2_opt,inffunc,meanfunc,covfunc,likfunc,x,y,xstar)
ym = vargout[0]; ys2 = vargout[1]; m = vargout[2]; s2 = vargout[3]
## Plot results
if PLOT:
plotter(xstar,ym,ys2,x,y,[-1.9, 1.9, -0.9, 3.9])
plt.grid()
plt.axis([-4, 4, -4, 4])
plt.show()
## DEFINE parameterized mean and covariance functions
meanfunc = ['means.meanConst']
covfunc = ['kernels.covSEard']
## DEFINE likelihood function used
likfunc = ['likelihoods.likErf']
## 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:
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)
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)
vargout = gp(hyp, inffunc, meanfunc, covfunc, likfunc, x, y,
np.concatenate((x, xs), axis=0))
ym = vargout[0]
ys2 = vargout[1]
m = vargout[2]
s2 = vargout[3]
print 'Time to optimize = ', t1 - t0
print 'Optimized mean = ', hyp.mean
print 'Optimized covariance = ', hyp.cov
print 'Optimized liklihood = ', hyp.lik
plt.axis([-4, 4, -4, 4])
plt.show()
## DEFINE parameterized mean and covariance functions
meanfunc = ['means.meanConst']
covfunc = ['kernels.covSEard']
## DEFINE likelihood function used
likfunc = ['likelihoods.likErf']
## 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)))
plotter(xstar, ym, ys2, x, y, [-2, 2, -0.9, 3.9])
## GET negative log marginal likelihood
[nlml, post] = gp(hyp2, inffunc, meanfunc, covfunc, likfunc, x, y, None,
None, False)
print "nlml =", nlml
##----------------------------------------------------------##
## STANDARD GP (example 3) ##
##----------------------------------------------------------##
print '...example 3: training and prediction...'
## TRAINING: OPTIMIZE HYPERPARAMETERS
## -> parameter training via off-the-shelf optimization
t0 = clock()
[hyp2_opt, fopt, gopt,
funcCalls] = min_wrapper(hyp2, gp, 'Minimize', inffunc, meanfunc, covfunc,
likfunc, x, y, None, None, True) # minimize
#[hyp2_opt, fopt, gopt, funcCalls] = min_wrapper(hyp2,gp,'CG',inffunc,meanfunc,covfunc,likfunc,x,y,None,None,True) # conjugent gradient
#[hyp2_opt, fopt, gopt, funcCalls] = min_wrapper(hyp2,gp,'SCG',inffunc,meanfunc,covfunc,likfunc,x,y,None,None,True) # scaled conjugent gradient (faster than CG)
#[hyp2_opt, fopt, gopt, funcCalls] = min_wrapper(hyp2,gp,'BFGS',inffunc,meanfunc,covfunc,likfunc,x,y,None,None,True) # quasi-Newton method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS)
t1 = clock()
print 'Time for optimization =', t1 - t0
print "Optimal nlml =", fopt
## PREDICTION
vargout = gp(hyp2_opt, inffunc, meanfunc, covfunc, likfunc, x, y, xstar)
ym = vargout[0]
ys2 = vargout[1]
m = vargout[2]
s2 = vargout[3]
## Plot results