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Tutorial improved (and finished)

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Nicolas 2013-02-21 12:28:35 +00:00
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16
doc/tuto_kernel_overview.rst
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@ -24,7 +24,7 @@ A ``print`` and a ``plot`` functions are implemented to represent kernel objects
ker2.plot()
ker3.plot()
should return::
return::
Name | Value | Constraints | Ties
-------------------------------------------------------
@ -49,12 +49,12 @@ On the other hand, it is possible to use the `sympy` package to build new kernel
Operations to combine kernels
=============================
In ``GPy``, two kernel objects can be added or multiplied. In both cases, two kinds of operations are possible since one can assume that the kernels to add/multiply are defined on the same space or on different subspaces. In other words, it is possible to use two kernels :math:`k_1,\ k_2` over :math:`\mathbb{R} \times \mathbb{R}` to create
In ``GPy``, kernel objects can be added or multiplied. In both cases, two kinds of operations are possible since one can assume that the kernels to add/multiply are defined on the same space or on different subspaces. In other words, it is possible to use two kernels :math:`k_1,\ k_2` over :math:`\mathbb{R} \times \mathbb{R}` to create
* a kernel over :math:`\mathbb{R} \times \mathbb{R}`: :math:`k(x,y) = k_1(x,y) \times k_2(x,y)`
* a kernel over :math:`\mathbb{R}^2 \times \mathbb{R}^2`: :math:`k(x,y) = k_1(x_1,y_1) \times k_2(x_2,y_2)`
* a kernel over :math:`\mathbb{R}^2 \times \mathbb{R}^2`: :math:`k(\mathbf{x},\mathbf{y}) = k_1(x_1,y_1) \times k_2(x_2,y_2)`
These two options are available in GPy under the name ``prod`` and ``prod_orthogonal`` (resp ``add`` and ``add_orthogonal`` for the addition). Here is a quick example ::
These two options are available in GPy under the name ``prod`` and ``prod_orthogonal`` (resp. ``add`` and ``add_orthogonal`` for the addition). Here is a quick example ::
k1 = GPy.kern.rbf(1,1.,2.)
k2 = GPy.kern.Matern32(1, 0.5, 0.2)
@ -112,11 +112,15 @@ A shortcut for ``add`` and ``prod`` is provided by the usual ``+`` and ``*`` ope
:align: center
:height: 300px
In general, ``kern`` objects can be seen as a sum of ``kernparts`` objects, where the later are covariance functions denied on the same space ::
k = (k1+k2)*(k1+k2)
print k.parts[0].name, '\n', k.parts[1].name, '\n', k.parts[2].name, '\n', k.parts[3].name
Constraining the parameters
===========================
Various constrains can be applied to the parameters of a kernel::
Various constrains can be applied to the parameters of a kernel
* ``constrain_fixed`` to fix the value of a parameter (the value will not be modified during optimisation)
* ``constrain_positive`` to make sure the parameter is greater than 0.
@ -237,7 +241,7 @@ The submodels can be represented with the option ``which_function`` of ``plot``:
.. figure:: Figures/tuto_kern_overview_mANOVAdec.png
:align: center
:height: 300px
:height: 250px
.. import pylab as pb