Offset model and clustering utility

GPy/models/gp_offset_regression.py

@@ -0,0 +1,92 @@
+# Copyright (c) 2012 - 2014 the GPy Austhors (see AUTHORS.txt)
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+# Written by Mike Smith. michaeltsmith.org.uk
+
+import numpy as np
+from ..core import GP
+from .. import likelihoods
+from .. import kern
+from ..core import Param
+
+class GPOffsetRegression(GP):
+    """
+    Gaussian Process model for offset regression
+
+    :param X: input observations, we assume for this class that this has one dimension of actual inputs and the last dimension should be the index of the cluster (so X should be Nx2)
+    :param Y: observed values (Nx1?)
+    :param kernel: a GPy kernel, defaults to rbf
+    :param Norm normalizer: [False]
+    :param noise_var: the noise variance for Gaussian likelhood, defaults to 1.
+
+        Normalize Y with the norm given.
+        If normalizer is False, no normalization will be done
+        If it is None, we use GaussianNorm(alization)
+
+    .. Note:: Multiple independent outputs are allowed using columns of Y
+
+    """
+
+    def __init__(self, X, Y, kernel=None, Y_metadata=None, normalizer=None, noise_var=1., mean_function=None):
+
+        assert X.shape[1]>1, "Need at least two input dimensions, as last dimension is the label of the cluster"
+        if kernel is None:
+            kernel = kern.RBF(X.shape[1]-1)
+
+        #self._log_marginal_likelihood = np.nan #todo
+        
+        likelihood = likelihoods.Gaussian(variance=noise_var)
+        self.X_fixed = X[:,:-1]
+        self.selected = np.array([int(x) for x in X[:,-1]])
+        
+        
+        super(GPOffsetRegression, self).__init__(X, Y, kernel, likelihood, name='GP offset regression', Y_metadata=Y_metadata, normalizer=normalizer, mean_function=mean_function)
+        maxcluster = np.max(self.selected)
+        self.offset = Param('offset', np.zeros(maxcluster))
+        #self.offset.set_prior(...)
+        self.link_parameter(self.offset)
+        
+    #def dr_doffset(self, X, sel): #how much r changes wrt the offset hyperparameters
+        
+    #def dL_doffset(self, X, sel):
+    #    dL_dr = self.dK_dr_via_X(X, X) * dL_dK
+        
+        
+        
+    def dr_doffset(self,X,sel,delta):
+        #given an input matrix, X and the offsets (delta)
+        #finds dr/dDelta
+        #returns them as a list, one for each offset (delta).        
+        #get the input values
+
+        #a matrix G represents the effect of increasing the offset on the radius passed to the kernel for each input. For example
+        #what effect will increasing offset 4 have on the kernel output of inputs 5 and 8? Answer: Gs[4][5,8]... (positive or negative)
+        Gs = []
+        for i,d in enumerate(delta):
+            #X[sel==(i+1)]-=d
+            G = np.repeat(np.array(sel==(i+1))[:,None]*1,len(X),axis=1) - np.repeat(np.array(sel==(i+1))[None,:]*1,len(X),axis=0)
+            Gs.append(G)
+        #does subtracting the two Xs end up positive or negative (if negative we need to flip the sign in G).
+        w = np.repeat(X,len(X),axis=1) - np.repeat(X.T,len(X),axis=0)
+        dr_doffsets = []
+        for i,d in enumerate(delta):
+            dr_doffset = np.sign(w * Gs[i])
+            #print "dr_doffset %d" % i
+            #print dr_doffset
+            #print Gs[i]
+            #print w
+            dr_doffsets.append(dr_doffset)
+        return dr_doffsets
+        
+    def parameters_changed(self):
+        offsets = np.hstack([0.0,self.offset.values])[:,None]
+        
+        self.X = self.X_fixed - offsets[self.selected]
+        super(GPOffsetRegression, self).parameters_changed()
+        
+        dL_dr = self.kern.dK_dr_via_X(self.X, self.X) * self.grad_dict['dL_dK']
+        
+        dr_doff = self.dr_doffset(self.X,self.selected,self.offset.values)
+        for i in range(len(dr_doff)):
+            dL_doff = dL_dr * dr_doff[i]
+            self.offset.gradient[i] = -np.sum(dL_doff)
+