def gp_ex_fig_22():
"""Similar to figure 2.2 in `Gaussian Processes for Machine Learning`__ by Rasmussen and Williams.
__ http://www.amazon.co.uk/Gaussian-Processes-Learning-Adaptive-Computation/dp/026218253X/
"""
X = [
[ -4.0 ],
[ -3.0 ],
[ -1.0 ],
[ 0.0 ],
[ 2.0 ],
]
y = numpy.array( [
-2.0,
0.0,
1.0,
2.0,
-1.0
] )
LN = infpy.LogNormalDistribution
Gamma = infpy.GammaDistribution
k = (
infpy.noise_kernel( .2, Gamma( 1.0, 1.0 ) )
+ infpy.ConstantKernel( )
* infpy.SquaredExponentialKernel( [ 1.0 ], [ LN() ] )
)
gp = infpy.GaussianProcess( X, y, k )
#infpy.gp_1D_predict( gp, 100, x_min = -5.0, x_max = 5.0 )
infpy.gp_learn_hyperparameters( gp )
infpy.gp_1D_predict( gp, 100, x_min = -5.0, x_max = 5.0 )
def gp_ex_output_scale():
"""Examine how kernel parameters should change for scaled outputs"""
start, end = 0.0, 1.0
X = infpy.gp_1D_X_range( start, end, 0.04 )
noise_level = 0.1
small_y = infpy.gp_zero_mean(
numpy.asarray(
[ x[0]**2 + noise_level * scipy.stats.norm().rvs()[0] for x in X ]
)
)
# big_y = small_y * 100.0
LN = infpy.LogNormalDistribution
k = (
infpy.noise_kernel( noise_level, LN( math.log( math.sqrt( noise_level ) ) ) )
+ infpy.ConstantSquaredKernel( 1.0, LN( math.log( 1.0 ) ) )
* infpy.SquaredExponentialKernel( [ 1.0 ], [ LN() ] )
)
gp = infpy.GaussianProcess( X, small_y, k )
infpy.gp_1D_predict( gp, 100 )
infpy.gp_learn_hyperparameters( gp )
infpy.gp_1D_predict( gp, 100 )
def gp_ex_fixed_period_1():
"""Example of the fixed period kernel"""
start, end = 0.0, 4.0
X = infpy.gp_1D_X_range( start, end, 0.4 )
y = numpy.asarray( [ math.sin( 2.0 * math.pi * x[0] ) for x in X ] )
# pylab.plot( [ x[0] for x in X ], [ y1 for y1 in y ] )
# pylab.show()
# return
LN = infpy.LogNormalDistribution
Gamma = infpy.GammaDistribution
k = (
infpy.noise_kernel( 0.1, LN( ) )
+ infpy.ConstantKernel( 1.0, Gamma( ) )
* infpy.FixedPeriod1DKernel( 1.0 )
)
gp = infpy.GaussianProcess( X, y, k )
infpy.gp_learn_hyperparameters( gp )
infpy.gp_1D_predict( gp )
if display:
from pylab import figure, plot, show, fill, title
figure()
infpy.gp_plot_prediction( test_x, f_star_mean, V_f_star )
plot(
[ x[0] for (x, v) in training_points ],
[ v for (x, v) in training_points ],
'rs' )
infpy.gp_title_and_show( gp )
#
# Learn hyperparameters
#
predict_values( display = True )
#sys.exit()
# print 'Params:', gp.k.get_parameters()
for initial_guess in [
# [ 10.0 ],
# [ 0.01 ],
[ 0.01, 10.0 ],
[ 0.01, 0.01 ],
None,
]:
print 'Learning from initial parameters:', initial_guess
infpy.gp_learn_hyperparameters( gp, initial_guess )
print dir(gp)
print 'Learnt parameters: %s\nLL: %f' \
% ( str( gp.k.params ), gp.LL )
predict_values( display = True )
