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():
"""Example of the fixed period kernel"""
start, end = -4.0, 0.0
X = infpy.gp_1D_X_range( start, end, 1.3 )
# X = [ ]
# X = [ [ 0.0 ] ]
# X = [ [ 0.0 ], [ 1.0 ] ]
# X = [ [ 0.0 ], [ -1.0 ], [ -2.0 ], [ -3.0 ], ]
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()
LN = infpy.LogNormalDistribution
k = (
infpy.FixedPeriod1DKernel( 1.0 )
+ infpy.noise_kernel( 0.1 )
)
gp = infpy.GaussianProcess( X, y, k )
sample_X = infpy.gp_1D_X_range( start, end, 0.03 )
y = infpy.gp_sample_from( gp, sample_X )
( y, V_f_star, log_p_y_given_X ) = gp.predict( sample_X )
infpy.gp_plot_prediction( sample_X, y )
infpy.gp_title_and_show( gp )
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 )
