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Tutorial improved

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Nicolas 2013-02-21 12:10:08 +00:00
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doc/tuto_kernel_overview.rst
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@ -44,15 +44,10 @@ Many kernels are already implemented in GPy. Here is a summary of most of them:
:align: center
:height: 800px
On the other hand, it is possible to use the `sympy` package to build new kernels. This will be the subject of another tutorial.
On the other hand, it is possible to use the `sympy` package to build new kernels. This will be the subject of another tutorial.
Constraining the parameters
===========================
Operations to combine 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
@ -117,6 +112,53 @@ A shortcut for ``add`` and ``prod`` is provided by the usual ``+`` and ``*`` ope
:align: center
:height: 300px
Constraining the parameters
===========================
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.
* ``constrain_bounded`` to impose the parameter to be in a given range.
* ``tie_param`` to impose the value of two (or more) parameters to be equal.
When calling one of these functions, the parameters to constrain can either by specified by a regular expression that matches its name or by a number that corresponds to the rank of the parameter. Here is an example ::
k1 = GPy.kern.rbf(1)
k2 = GPy.kern.Matern32(1)
k3 = GPy.kern.white(1)
k = k1 + k2 + k3
print k
k.constrain_positive('var')
k.constrain_fixed(np.array([1]),1.75)
k.tie_param('len')
k.unconstrain('white')
k.constrain_bounded('white',lower=1e-5,upper=.5)
print k
with output::
Name | Value | Constraints | Ties
---------------------------------------------------------
rbf_variance | 1.0000 | |
rbf_lengthscale | 1.0000 | |
Mat32_variance | 1.0000 | |
Mat32_lengthscale | 1.0000 | |
white_variance | 1.0000 | |
Name | Value | Constraints | Ties
----------------------------------------------------------
rbf_variance | 1.0000 | (+ve) |
rbf_lengthscale | 1.7500 | Fixed | (0)
Mat32_variance | 1.0000 | (+ve) |
Mat32_lengthscale | 1.7500 | | (0)
white_variance | 0.3655 | (1e-05, 0.5) |
Example : Building an ANOVA kernel
==================================