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Few changes to tutorial

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Nicolas 2013-02-08 16:22:29 +00:00
parent bc62b79e49
commit a33dff924b
1 changed files with 40 additions and 45 deletions
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doc/tuto_kernel_overview.rst
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@ -12,7 +12,7 @@ First we import the libraries we will need ::
For most kernels, the dimension is the only mandatory parameter to define a kernel object. However, it is also possible to specify the values of the parameters. For example, the three following commands are valid for defining a squared exponential kernel (ie rbf or Gaussian) ::
ker1 = GPy.kern.rbf(D=1) # Equivalent to ker1 = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
ker1 = GPy.kern.rbf(1) # Equivalent to ker1 = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
ker2 = GPy.kern.rbf(D=1, variance = 1.5, lengthscale=2.)
ker3 = GPy.kern.rbf(1, .5, .5)
@ -28,43 +28,6 @@ A `plot` and a `print` functions are implemented to represent kernel objects ::
:align: center
:height: 350px
::
import pylab as pb
import numpy as np
import GPy
pb.ion()
ker1 = GPy.kern.rbf(D=1) # Equivalent to ker1 = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
ker2 = GPy.kern.rbf(D=1, variance = .75, lengthscale=3.)
ker3 = GPy.kern.rbf(1, .5, .25)
ker1.plot()
ker2.plot()
ker3.plot()
#pb.savefig("Figures/tuto_kern_overview_basicdef.png")
kernels = [GPy.kern.rbf(1), GPy.kern.exponential(1), GPy.kern.Matern32(1), GPy.kern.Matern52(1), GPy.kern.Brownian(1), GPy.kern.bias(1), GPy.kern.linear(1), GPy.kern.spline(1), GPy.kern.periodic_exponential(1), GPy.kern.periodic_Matern32(1), GPy.kern.periodic_Matern52(1), GPy.kern.white(1)]
kernel_names = ["GPy.kern.rbf", "GPy.kern.exponential", "GPy.kern.Matern32", "GPy.kern.Matern52", "GPy.kern.Brownian", "GPy.kern.bias", "GPy.kern.linear", "GPy.kern.spline", "GPy.kern.periodic_exponential", "GPy.kern.periodic_Matern32", "GPy.kern.periodic_Matern52", "GPy.kern.white"]
pb.figure(figsize=(16,12))
pb.subplots_adjust(wspace=.5, hspace=.5)
for i, kern in enumerate(kernels):
pb.subplot(3,4,i+1)
kern.plot(x=7.5,plot_limits=[0.00001,15.])
pb.title(kernel_names[i]+ '\n')
#pb.axes([.1,.1,.8,.7])
#pb.figtext(.5,.9,'Foo Bar', fontsize=18, ha='center')
#pb.figtext(.5,.85,'Lorem ipsum dolor sit amet, consectetur adipiscing elit',fontsize=10,ha='center')
# actual plot for the noise
i = 11
X = np.linspace(0.,15.,201)
WN = 0*X
WN[100] = 1.
pb.subplot(3,4,i+1)
pb.plot(X,WN,'b')
Implemented kernels
===================
@ -90,22 +53,18 @@ In ``GPy``, kernel objects can be combined with the usual ``+`` and ``*`` operat
ker_prod = k1 * k2
print ker_prod
Note that by default, the operator ``+`` adds kernels defined on the same input space whereas ``*`` assumes that the kernels are defined on different input spaces. ::
ker_add.D
ker_prod.D
Note that by default, the operator ``+`` adds kernels defined on the same input space whereas ``*`` assumes that the kernels are defined on different input spaces. Here for example ``ker_add.D`` will return ``1`` whereas ``ker_prod.D`` will return ``2``.
In order to add kernels defined on the different input spaces, the required command is::
ker_add_orth = k1.add_orthogonal(k2)
The resulting kernel is
ker_add_orth.plot(plot_limits=[[-10,-10],[10,10]])
.. figure:: Figures/tuto_kern_overview_add_orth.png
:align: center
:height: 350px
Output of ``ker_add_orth.plot(plot_limits=[[-10,-10],[10,10]])``.
Example : Building an ANOVA kernel
==================================
@ -167,3 +126,39 @@ The submodels can be represented with the option ``which_function`` of ``plot``:
.. figure:: Figures/tuto_kern_overview_mANOVAdec.png
:align: center
:height: 200px
.. import pylab as pb
import numpy as np
import GPy
pb.ion()
ker1 = GPy.kern.rbf(D=1) # Equivalent to ker1 = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
ker2 = GPy.kern.rbf(D=1, variance = .75, lengthscale=3.)
ker3 = GPy.kern.rbf(1, .5, .25)
ker1.plot()
ker2.plot()
ker3.plot()
#pb.savefig("Figures/tuto_kern_overview_basicdef.png")
kernels = [GPy.kern.rbf(1), GPy.kern.exponential(1), GPy.kern.Matern32(1), GPy.kern.Matern52(1), GPy.kern.Brownian(1), GPy.kern.bias(1), GPy.kern.linear(1), GPy.kern.spline(1), GPy.kern.periodic_exponential(1), GPy.kern.periodic_Matern32(1), GPy.kern.periodic_Matern52(1), GPy.kern.white(1)]
kernel_names = ["GPy.kern.rbf", "GPy.kern.exponential", "GPy.kern.Matern32", "GPy.kern.Matern52", "GPy.kern.Brownian", "GPy.kern.bias", "GPy.kern.linear", "GPy.kern.spline", "GPy.kern.periodic_exponential", "GPy.kern.periodic_Matern32", "GPy.kern.periodic_Matern52", "GPy.kern.white"]
pb.figure(figsize=(16,12))
pb.subplots_adjust(wspace=.5, hspace=.5)
for i, kern in enumerate(kernels):
pb.subplot(3,4,i+1)
kern.plot(x=7.5,plot_limits=[0.00001,15.])
pb.title(kernel_names[i]+ '\n')
#pb.axes([.1,.1,.8,.7])
#pb.figtext(.5,.9,'Foo Bar', fontsize=18, ha='center')
#pb.figtext(.5,.85,'Lorem ipsum dolor sit amet, consectetur adipiscing elit',fontsize=10,ha='center')
# actual plot for the noise
i = 11
X = np.linspace(0.,15.,201)
WN = 0*X
WN[100] = 1.
pb.subplot(3,4,i+1)
pb.plot(X,WN,'b')