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Added ANOVA kernel print output

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Alan Saul 2013-02-10 16:21:19 +00:00
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15
doc/tuto_kernel_overview.rst
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@ -74,13 +74,26 @@ In two dimensions ANOVA kernels have the following form:
k_{ANOVA}(x,y) = \prod_{i=1}^2 (1 + k_i(x_i,y_i)) = 1 + k_1(x_1,y_1) + k_2(x_2,y_2) + k_1(x_1,y_1) \times k_2(x_2,y_2).
Let us assume that we want to define an ANOVA kernel with a Matern 3/2 kernel for :math:`k_i`. As seen previously, we can define this kernel as follow::
Let us assume that we want to define an ANOVA kernel with a Matern 3/2 kernel for :math:`k_i`. As seen previously, we can define this kernel as follows ::
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)
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)
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::
# sample inputs and outputs