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Tutorial improved

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Nicolas 2013-02-21 11:40:41 +00:00
parent 58f84f197e
commit e47dc5b4ab
4 changed files with 22 additions and 17 deletions
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39
doc/tuto_kernel_overview.rst
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@ -33,7 +33,7 @@ should return::
.. figure:: Figures/tuto_kern_overview_basicplot.png
:align: center
:height: 350px
:height: 300px
Implemented kernels
===================
@ -105,7 +105,7 @@ A shortcut for ``add`` and ``prod`` is provided by the usual ``+`` and ``*`` ope
Y = np.random.multivariate_normal(np.zeros(501),k.K(X),1)
.. # plot
pb.figure(figsize=(8,4))
pb.figure(figsize=(10,4))
pb.subplot(1,2,1)
k.plot()
pb.subplot(1,2,2)
@ -115,7 +115,7 @@ A shortcut for ``add`` and ``prod`` is provided by the usual ``+`` and ``*`` ope
.. figure:: Figures/tuto_kern_overview_multperdecay.png
:align: center
:height: 350px
:height: 300px
Example : Building an ANOVA kernel
==================================
@ -130,23 +130,27 @@ Let us assume that we want to define an ANOVA kernel with a Matern 3/2 kernel fo
k_cst = GPy.kern.bias(1,variance=1.)
k_mat = GPy.kern.Matern52(1,variance=1., lengthscale=3)
Kanova = (k_cst + k_mat) * (k_cst + k_mat)
Kanova = (k_cst + k_mat).prod_orthogonal(k_cst + k_mat)
print Kanova
Printing the resulting kernel outputs the following ::
Name | Value | Constraints | Ties
---------------------------------------------------------------------------
bias<times>bias_variance | 1.0000 | |
bias<times>Mat52_variance | 1.0000 | |
bias<times>Mat52_Mat52_lengthscale | 3.0000 | | (1)
Mat52<times>bias_variance | 1.0000 | |
Mat52<times>bias_Mat52_lengthscale | 3.0000 | | (0)
Mat52<times>Mat52_variance | 1.0000 | |
Mat52<times>Mat52_Mat52_lengthscale | 3.0000 | | (0)
Mat52<times>Mat52_Mat52_lengthscale | 3.0000 | | (1)
bias<times>bias_bias_variance | 1.0000 | | (0)
bias<times>bias_bias_variance | 1.0000 | | (3)
bias<times>Mat52_bias_variance | 1.0000 | | (0)
bias<times>Mat52_Mat52_variance | 1.0000 | | (4)
bias<times>Mat52_Mat52_lengthscale | 3.0000 | | (5)
Mat52<times>bias_Mat52_variance | 1.0000 | | (1)
Mat52<times>bias_Mat52_lengthscale | 3.0000 | | (2)
Mat52<times>bias_bias_variance | 1.0000 | | (3)
Mat52<times>Mat52_Mat52_variance | 1.0000 | | (1)
Mat52<times>Mat52_Mat52_lengthscale | 3.0000 | | (2)
Mat52<times>Mat52_Mat52_variance | 1.0000 | | (4)
Mat52<times>Mat52_Mat52_lengthscale | 3.0000 | | (5)
Note the ties between the lengthscales of ``Kanova`` to keep the number of lengthscales equal to 2. On the other hand, there are four variance terms in the new parameterization: one for each term of the right hand part of the above equation. We can illustrate the use of this kernel on a toy example::
Note the ties between the parameters of ``Kanova`` that reflect the links between the parameters of the kernparts objects. We can illustrate the use of this kernel on a toy example::
# sample inputs and outputs
X = np.random.uniform(-3.,3.,(40,2))
@ -154,12 +158,12 @@ Note the ties between the lengthscales of ``Kanova`` to keep the number of lengt
# Create GP regression model
m = GPy.models.GP_regression(X,Y,Kanova)
pb.figure(figsize=(5,5))
m.plot()
.. figure:: Figures/tuto_kern_overview_mANOVA.png
:align: center
:height: 350px
:height: 300px
As :math:`k_{ANOVA}` corresponds to the sum of 4 kernels, the best predictor can be splited in a sum of 4 functions
@ -171,7 +175,7 @@ As :math:`k_{ANOVA}` corresponds to the sum of 4 kernels, the best predictor can
The submodels can be represented with the option ``which_function`` of ``plot``: ::
pb.figure(figsize=(20,5))
pb.figure(figsize=(20,3))
pb.subplots_adjust(wspace=0.5)
pb.subplot(1,5,1)
m.plot()
@ -187,10 +191,11 @@ The submodels can be represented with the option ``which_function`` of ``plot``:
pb.ylabel("+ ",rotation='horizontal',fontsize='30')
m.plot(which_functions=[False,False,False,True])
.. pb.savefig('tuto_kern_overview_mANOVAdec.png',bbox_inches='tight')
.. figure:: Figures/tuto_kern_overview_mANOVAdec.png
:align: center
:height: 200px
:height: 300px
.. import pylab as pb