From e47dc5b4ab194c52e28c1ec2128e9fd5f15772e4 Mon Sep 17 00:00:00 2001 From: Nicolas Date: Thu, 21 Feb 2013 11:40:41 +0000 Subject: [PATCH] Tutorial improved --- doc/Figures/tuto_kern_overview_mANOVA.png | Bin 56323 -> 38088 bytes doc/Figures/tuto_kern_overview_mANOVAdec.png | Bin 86347 -> 79486 bytes .../tuto_kern_overview_multperdecay.png | Bin 37033 -> 40904 bytes doc/tuto_kernel_overview.rst | 39 ++++++++++-------- 4 files changed, 22 insertions(+), 17 deletions(-) diff --git a/doc/Figures/tuto_kern_overview_mANOVA.png b/doc/Figures/tuto_kern_overview_mANOVA.png index db49e3bd762dc2727fad1e90d492e99544df5aba..f7ff5f503fef6ce878947e5b3c7eff64339ce66d 100644 GIT binary patch literal 38088 zcmeEtWm8;D)a~GI!DWy@kYK@GL$KiP8r)@YOR(S&65QP-xVyUrcXxNYhv%)g?$`SR zE>%-!hMCj7yU*_3d#|-RL_tmh4VefT1OlN+Ns1|fK+wQjXb>ViaJh1uegH18PNGsO zh`^s0;zx+#zRAwB zaWwuXxPGd!#KcD@-3DkUY9}8<$x-jLA~vE3@c>LwL__7PA{a!90L-i>DJXK_KXc@C zptmoGso?zHzW2`o0T&AEXdDo52|)V=Eeu>LM3g{pcX3K0gMdpX{QtlC|8c_l^&lWs 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a/doc/tuto_kernel_overview.rst b/doc/tuto_kernel_overview.rst index 6c818648..7dd918da 100644 --- a/doc/tuto_kernel_overview.rst +++ b/doc/tuto_kernel_overview.rst @@ -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 --------------------------------------------------------------------------- - biasbias_variance | 1.0000 | | - biasMat52_variance | 1.0000 | | - biasMat52_Mat52_lengthscale | 3.0000 | | (1) - Mat52bias_variance | 1.0000 | | - Mat52bias_Mat52_lengthscale | 3.0000 | | (0) - Mat52Mat52_variance | 1.0000 | | - Mat52Mat52_Mat52_lengthscale | 3.0000 | | (0) - Mat52Mat52_Mat52_lengthscale | 3.0000 | | (1) + biasbias_bias_variance | 1.0000 | | (0) + biasbias_bias_variance | 1.0000 | | (3) + biasMat52_bias_variance | 1.0000 | | (0) + biasMat52_Mat52_variance | 1.0000 | | (4) + biasMat52_Mat52_lengthscale | 3.0000 | | (5) + Mat52bias_Mat52_variance | 1.0000 | | (1) + Mat52bias_Mat52_lengthscale | 3.0000 | | (2) + Mat52bias_bias_variance | 1.0000 | | (3) + Mat52Mat52_Mat52_variance | 1.0000 | | (1) + Mat52Mat52_Mat52_lengthscale | 3.0000 | | (2) + Mat52Mat52_Mat52_variance | 1.0000 | | (4) + Mat52Mat52_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