optimize its hyperparameters.
"""
import os
import numpy as np
import matplotlib.pyplot as pl
import pygp
import pygp.plotting as pp
if __name__ == '__main__':
# load the data.
cdir = os.path.abspath(os.path.dirname(__file__))
data = np.load(os.path.join(cdir, 'xy.npz'))
X = data['X']
y = data['y']
# create the model, add data, and optimize it.
gp = pygp.BasicGP(sn=.1, sf=1, ell=.1, mu=0)
gp.add_data(X, y)
pygp.optimize(gp)
# plot the posterior.
pl.figure(1)
pl.clf()
pp.plot_posterior(gp)
pl.legend(loc=2)
pl.draw()
pl.show()
# create a prior structure.
priors = {
'sn': pygp.priors.Uniform(0.01, 1.0),
'sf': pygp.priors.Uniform(0.01, 5.0),
'ell': pygp.priors.Uniform(0.01, 1.0),
'mu': pygp.priors.Uniform(-2, 2)}
# create sample-based models.
mcmc = pygp.meta.MCMC(model, priors, n=200, burn=100)
smc = pygp.meta.SMC(model, priors, n=200)
pl.figure(1)
pl.clf()
pl.subplot(131)
pp.plot_posterior(model)
pl.title('Type-II ML')
pl.legend(loc='best')
axis = pl.axis()
pl.subplot(132)
pp.plot_posterior(mcmc)
pl.axis(axis)
pl.title('MCMC')
pl.subplot(133)
pp.plot_posterior(mcmc)
pl.axis(axis)
pl.title('SMC')
pl.draw()
# create a sparse GPs.
U = np.linspace(-1.3, 2, 10)[:, None]
gp2 = pygp.inference.FITC.from_gp(gp1, U)
gp3 = pygp.inference.DTC.from_gp(gp1, U)
# find the ML parameters
pygp.optimize(gp1)
pygp.optimize(gp2)
pygp.optimize(gp3)
# plot the dense gp.
pl.figure(1)
pl.clf()
pl.subplot(131)
pp.plot_posterior(gp1)
pl.title("Full GP")
# grab the axis limits.
axis = pl.axis()
# plot the FITC sparse gp.
pl.subplot(132)
pp.plot_posterior(gp2, pseudoinputs=True)
pl.title("Sparse GP (FITC)")
pl.axis(axis)
pl.draw()
# plot the sparse gp.
pl.subplot(133)
pp.plot_posterior(gp3, pseudoinputs=True)
def test_plot_posterior():
gp = pygp.BasicGP(1, 1, 1)
gp = pygp.inference.FITC.from_gp(gp, mr.grid((0, 1), 10))
nt.assert_raises(ValueError, pg.plot_posterior, gp)
pg.plot_posterior(gp, 0, 1)
pg.plot_posterior(gp, 0, 1, error=False)
pg.plot_posterior(gp, 0, 1, mean=False)
pg.plot_posterior(gp, 0, 1, data=False)
pg.plot_posterior(gp, 0, 1, pseudoinputs=False)
pg.plot_posterior(gp, 0, 1, color='b')
pg.plot_posterior(gp, 0, 1, lw=3)
pg.plot_posterior(gp, 0, 1, ls='.')
X = mr.grid((0, 1), 10)
y = np.random.rand(10)
gp.add_data(X, y)
pg.plot_posterior(gp)
if __name__ == "__main__":
# load the file from the current directory and get rid of any censored data.
cdir = os.path.abspath(os.path.dirname(__file__))
data = np.loadtxt(os.path.join(cdir, "maunaloa.txt")).flatten()
data = np.array([(x, y) for x, y in enumerate(data) if y > -99])
# minor manipulations of the data to make the ranges reasonable.
X = data[:, 0, None] / 12.0 + 1958
y = data[:, 1]
# these are near the values called for in Rasmussen and Williams, so they
# should give reasonable results and thus we'll skip the fit.
kernel = pk.SE(67, 66) + pk.SE(2.4, 90) * pk.Periodic(1, 1, 1) + pk.RQ(1.2, 0.66, 0.78) + pk.SE(0.15, 0.15)
# use a gaussian likeihood with this standard deviation.
likelihood = pygp.likelihoods.Gaussian(sigma=0.2)
# construct the model and add the data.
gp = pygp.inference.ExactGP(likelihood, kernel, y.mean())
gp.add_data(X, y)
# plot everything.
pl.figure(1)
pl.clf()
pp.plot_posterior(gp, mean=False, xmax=2020, marker=".")
pl.legend(loc="upper left")
pl.draw()
pl.show()
priors = {
'sn': pygp.priors.Uniform(0.01, 1.0),
'sf': pygp.priors.Uniform(0.01, 5.0),
'ell': pygp.priors.Uniform(0.01, 1.0),
'mu': pygp.priors.Uniform(-2, 2)
}
# create sample-based models.
mcmc = pygp.meta.MCMC(model, priors, n=200, burn=100)
smc = pygp.meta.SMC(model, priors, n=200)
pl.figure(1)
pl.clf()
pl.subplot(131)
pp.plot_posterior(model)
pl.title('Type-II ML')
pl.legend(loc='best')
axis = pl.axis()
pl.subplot(132)
pp.plot_posterior(mcmc)
pl.axis(axis)
pl.title('MCMC')
pl.subplot(133)
pp.plot_posterior(mcmc)
pl.axis(axis)
pl.title('SMC')
pl.draw()
Basic demo showing how to instantiate a simple GP model, add data to it, and
optimize its hyperparameters.
"""
import os
import numpy as np
import matplotlib.pyplot as pl
import pygp
import pygp.plotting as pp
if __name__ == '__main__':
# load the data.
cdir = os.path.abspath(os.path.dirname(__file__))
data = np.load(os.path.join(cdir, 'xy.npz'))
X = data['X']
y = data['y']
# create the model, add data, and optimize it.
gp = pygp.BasicGP(sn=.1, sf=1, ell=.1, mu=0)
gp.add_data(X, y)
pygp.optimize(gp)
# plot the posterior.
pl.figure(1)
pl.clf()
pp.plot_posterior(gp)
pl.legend(loc=2)
pl.draw()
pl.show()
