Merge branch 'master' of github.com:SheffieldML/GPy

doc/GPy.testing.rst

@@ -0,0 +1,59 @@
+testing Package
+===============
+
+:mod:`bgplvm_tests` Module
+--------------------------
+
+.. automodule:: GPy.testing.bgplvm_tests
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+:mod:`examples_tests` Module
+----------------------------
+
+.. automodule:: GPy.testing.examples_tests
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+:mod:`gplvm_tests` Module
+-------------------------
+
+.. automodule:: GPy.testing.gplvm_tests
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+:mod:`kernel_tests` Module
+--------------------------
+
+.. automodule:: GPy.testing.kernel_tests
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+:mod:`prior_tests` Module
+-------------------------
+
+.. automodule:: GPy.testing.prior_tests
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+:mod:`sparse_gplvm_tests` Module
+--------------------------------
+
+.. automodule:: GPy.testing.sparse_gplvm_tests
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+:mod:`unit_tests` Module
+------------------------
+
+.. automodule:: GPy.testing.unit_tests
+    :members:
+    :undoc-members:
+    :show-inheritance:
+

doc/index.rst

@@ -10,8 +10,7 @@ For a quick start, you can have a look at one of the tutorials:
 * `Basic Gaussian process regression <tuto_GP_regression.html>`_  
 * `Interacting with models <tuto_interacting_with_models.html>`_
 * `A kernel overview <tuto_kernel_overview.html>`_ 
-* Advanced GP regression (Forthcoming)
-* Writing kernels (Forthcoming)
+* `Writing new kernels <tuto_creating_new_kernels.html>`_
 
 You may also be interested by some examples in the GPy/examples folder.
 

doc/tuto_creating_new_kernels.rst

@@ -0,0 +1,183 @@
+********************
+Creating new kernels
+********************
+
+We will see in this tutorial how to create new kernels in GPy. We will also give details on how to implement each function of the kernel and illustrate with a running example: the rational quadratic kernel. 
+
+Structure of a kernel in GPy
+============================
+
+In GPy a kernel object is made of a list of kernpart objects, which correspond to symetric positive definite functions. More precisely, the kernel should be understood as the sum of the kernparts. In order to implement a new covariance, the following steps must be followed
+
+    1. implement the new covariance as a kernpart object
+    2. update the constructors that allow to use the kernpart as a kern object
+    3. update the __init__.py file
+
+Theses three steps are detailed below.
+
+Implementing a kernpart object
+==============================
+
+We advise the reader to start with copy-pasting an existing kernel and to modify the new file. We will now give a description of the various functions that can be found in a kernpart object.
+
+**Header**
+
+The header is similar to all kernels: ::
+
+    from kernpart import kernpart
+    import numpy as np
+
+    class rational_quadratic(kernpart):
+
+**__init__(self,D, param1, param2, ...)**
+
+The implementation of this function in mandatory.
+
+For all kernparts the first parameter ``D`` corresponds to the dimension of the input space, and the following parameters stand for the parameterization of the kernel.
+
+The following attributes are compulsory: ``self.D`` (the dimension, integer), ``self.name`` (name of the kernel, string), ``self.Nparam`` (number of parameters, integer). ::
+
+    def __init__(self,D,variance=1.,lengthscale=1.,power=1.):
+        assert D == 1, "For this kernel we assume D=1"
+        self.D = D
+        self.Nparam = 3
+        self.name = 'rat_quad'
+        self.variance = variance
+        self.lengthscale = lengthscale
+        self.power = power
+
+**_get_params(self)**
+
+The implementation of this function in mandatory.
+
+This function returns a one dimensional array of length ``self.Nparam`` containing the value of the parameters. ::
+
+    def _get_params(self):
+        return np.hstack((self.variance,self.lengthscale,self.power))
+
+**_set_params(self,x)**
+
+The implementation of this function in mandatory.
+
+The input is a one dimensional array of length ``self.Nparam`` containing the value of the parameters. The function has no output but it updates the values of the attribute associated to the parameters (such as ``self.variance``, ``self.lengthscale``, ...). ::
+
+    def _set_params(self,x):
+        self.variance = x[0]
+        self.lengthscale = x[1]
+        self.power = x[2]
+
+**_get_param_names(self)**
+
+The implementation of this function in mandatory.
+
+It returns a list of strings of length ``self.Nparam`` corresponding to the parameter names. ::
+
+    def _get_param_names(self):
+        return ['variance','lengthscale','power']
+
+**K(self,X,X2,target)**
+
+The implementation of this function in mandatory.
+
+This function is used to compute the covariance matrix associated with the inputs X, X2 (np.arrays with arbitrary number of line (say :math:`n_1`, :math:`n_2`) and ``self.D`` columns). This function does not returns anything but it adds the :math:`n_1 \times n_2` covariance matrix to the kernpart to the object ``target`` (a :math:`n_1 \times n_2` np.array). This trick allows to compute the covariance matrix of a kernel containing many kernparts with a limited memory use. ::
+
+    def K(self,X,X2,target):
+        if X2 is None: X2 = X
+        dist2 = np.square((X-X2.T)/self.lengthscale)
+        target += self.variance*(1 + dist2/2.)**(-self.power)
+
+**Kdiag(self,X,target)**
+
+The implementation of this function in mandatory.
+
+This function is similar to ``K`` but it computes only the values of the kernel on the diagonal. Thus, ``target`` is a 1-dimensional np.array of length :math:`n_1`. ::
+
+    def Kdiag(self,X,target):
+        target += self.variance    
+
+
+**dK_dtheta(self,dL_dK,X,X2,target)**
+
+This function is required for the optimization of the parameters.
+
+Computes the derivative of the likelihood. As previously, the values are added to the object target which is a 1-dimensional np.array of length ``self.Nparam``. For example, if the kernel is parameterized by :math:`\sigma^2,\ \theta`, then :math:`\frac{dL}{d\sigma^2} = \frac{dL}{d K} \frac{dK}{d\sigma^2}` is added to the first element of target and :math:`\frac{dL}{d\theta} = \frac{dL}{d K} \frac{dK}{d\theta}` to the second. ::
+
+    def dK_dtheta(self,dL_dK,X,X2,target):
+        if X2 is None: X2 = X
+        dist2 = np.square((X-X2.T)/self.lengthscale)
+
+        dvar = (1 + dist2/2.)**(-self.power)
+        dl = self.power * self.variance * dist2 * self.lengthscale**(-3) * (1 + dist2/2./self.power)**(-self.power-1)
+        dp = - self.variance * np.log(1 + dist2/2.) * (1 + dist2/2.)**(-self.power)
+
+        target[0] += np.sum(dvar*dL_dK)
+        target[1] += np.sum(dl*dL_dK)
+        target[2] += np.sum(dp*dL_dK)
+
+
+**dKdiag_dtheta(self,dL_dKdiag,X,target)**
+
+This function is required for BGPLVM, sparse models and uncertain inputs.
+
+As previously, target is an ``self.Nparam`` array and :math:`\frac{dL}{d Kdiag} \frac{dKdiag}{dparam}` is added to each element. ::
+
+    def dKdiag_dtheta(self,dL_dKdiag,X,target):
+        target[0] += np.sum(dL_dKdiag)
+        # here self.lengthscale and self.power have no influence on Kdiag so target[1:] are unchanged
+
+**dK_dX(self,dL_dK,X,X2,target)**
+
+This function is required for GPLVM, BGPLVM, sparse models and uncertain inputs.
+
+Computes the derivative of the likelihood with respect to the inputs ``X`` (a :math:`n \times D` np.array). The result is added to target which is a :math:`n \times D` np.array. ::
+
+    def dK_dX(self,dL_dK,X,X2,target):
+        """derivative of the covariance matrix with respect to X."""
+        if X2 is None: X2 = X
+        dist2 = np.square((X-X2.T)/self.lengthscale)
+
+        dX = -self.variance*self.power * (X-X2.T)/self.lengthscale**2 *  (1 + dist2/2./self.power)**(-self.power-1)
+        target += np.sum(dL_dK*dX)
+
+**dKdiag_dX(self,dL_dKdiag,X,target)**
+
+This function is required for BGPLVM, sparse models and uncertain inputs. As for ``dKdiag_dtheta``, :math:`\frac{dL}{d Kdiag} \frac{dKdiag}{dX}` is added to each element of target. ::
+
+    def dKdiag_dX(self,dL_dKdiag,X,target):
+        pass
+
+**Psi statistics**
+
+The psi statistics and their derivatives are required for BGPLVM and GPS with uncertain inputs.
+
+The expressions of the psi statistics are:
+
+TODO
+
+For the rational quadratic we have:
+
+TODO
+
+Update the constructor 
+======================
+
+Once the required functions have been implemented as a kernpart object, the file GPy/kern/constructors.py has to be updated to allow to build a kernel based on the kernpart object.
+
+The following line should be added in the preamble of the file::
+
+    from rational_quadratic import rational_quadratic as rational_quadratic_part
+
+as well as the following block ::
+
+    def rational_quadratic(D,variance=1., lengthscale=1., power=1.):
+        part = rational_quadraticpart(D,variance, lengthscale, power)
+        return kern(D, [part])
+
+
+Update initialization
+=====================
+
+The last step is to update the list of kernels imported from constructor in GPy/kern/__init__.py.
+
+
+

doc/tuto_kernel_overview.rst

@@ -133,7 +133,7 @@ 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.
+    * ``tie_params`` 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 ::
 
@@ -146,7 +146,7 @@ When calling one of these functions, the parameters to constrain can either by s
 
     k.constrain_positive('var')
     k.constrain_fixed(np.array([1]),1.75)
-    k.tie_param('len')
+    k.tie_params('len')
     k.unconstrain('white')
     k.constrain_bounded('white',lower=1e-5,upper=.5)
     print k