coregionalisation

GPy/examples/regression.py

@@ -75,6 +75,74 @@ def silhouette():
     print(m)
     return m
 
+def coregionalisation_toy2():
+    """
+    A simple demonstration of coregionalisation on two sinusoidal functions
+    """
+    X1 = np.random.rand(50,1)*8
+    X2 = np.random.rand(30,1)*5
+    index = np.vstack((np.zeros_like(X1),np.ones_like(X2)))
+    X = np.hstack((np.vstack((X1,X2)),index))
+    Y1 = np.sin(X1) + np.random.randn(*X1.shape)*0.05
+    Y2 = np.sin(X2) + np.random.randn(*X2.shape)*0.05 + 2.
+    Y = np.vstack((Y1,Y2))
+
+    k1 = GPy.kern.rbf(1) + GPy.kern.bias(1)
+    k2 = GPy.kern.coregionalise(2,1)
+    k = k1.prod_orthogonal(k2)
+    m = GPy.models.GP_regression(X,Y,kernel=k)
+    m.constrain_fixed('rbf_var',1.)
+    m.constrain_positive('kappa')
+    m.ensure_default_constraints()
+    m.optimize()
+
+    pb.figure()
+    Xtest1 = np.hstack((np.linspace(0,9,100)[:,None],np.zeros((100,1))))
+    Xtest2 = np.hstack((np.linspace(0,9,100)[:,None],np.ones((100,1))))
+    mean, var,low,up = m.predict(Xtest1)
+    GPy.util.plot.gpplot(Xtest1[:,0],mean,low,up)
+    mean, var,low,up = m.predict(Xtest2)
+    GPy.util.plot.gpplot(Xtest2[:,0],mean,low,up)
+    pb.plot(X1[:,0],Y1[:,0],'rx',mew=2)
+    pb.plot(X2[:,0],Y2[:,0],'gx',mew=2)
+    return m
+
+
+
+
+def coregionalisation_toy():
+    """
+    A simple demonstration of coregionalisation on two sinusoidal functions
+    """
+    X1 = np.random.rand(50,1)*8
+    X2 = np.random.rand(30,1)*5
+    index = np.vstack((np.zeros_like(X1),np.ones_like(X2)))
+    X = np.hstack((np.vstack((X1,X2)),index))
+    Y1 = np.sin(X1) + np.random.randn(*X1.shape)*0.05
+    Y2 = -np.sin(X2) + np.random.randn(*X2.shape)*0.05
+    Y = np.vstack((Y1,Y2))
+
+    k1 = GPy.kern.rbf(1)
+    k2 = GPy.kern.coregionalise(2,1)
+    k = k1.prod_orthogonal(k2)
+    m = GPy.models.GP_regression(X,Y,kernel=k)
+    m.constrain_fixed('rbf_var',1.)
+    m.constrain_positive('kappa')
+    m.ensure_default_constraints()
+    m.optimize()
+
+    pb.figure()
+    Xtest1 = np.hstack((np.linspace(0,9,100)[:,None],np.zeros((100,1))))
+    Xtest2 = np.hstack((np.linspace(0,9,100)[:,None],np.ones((100,1))))
+    mean, var,low,up = m.predict(Xtest1)
+    GPy.util.plot.gpplot(Xtest1[:,0],mean,low,up)
+    mean, var,low,up = m.predict(Xtest2)
+    GPy.util.plot.gpplot(Xtest2[:,0],mean,low,up)
+    pb.plot(X1[:,0],Y1[:,0],'rx',mew=2)
+    pb.plot(X2[:,0],Y2[:,0],'gx',mew=2)
+    return m
+
+
 
 def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000):
     """Show an example of a multimodal error surface for Gaussian process regression. Gene 939 has bimodal behaviour where the noisey mode is higher."""
@@ -160,3 +228,4 @@ def contour_data(data, length_scales, log_SNRs, signal_kernel_call=GPy.kern.rbf)
             length_scale_lls.append(model.log_likelihood())
         lls.append(length_scale_lls)
     return np.array(lls)
+

GPy/kern/__init__.py

@@ -2,5 +2,5 @@
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 
 
-from constructors import rbf, Matern32, Matern52, exponential, linear, white, bias, finite_dimensional, spline, Brownian, rbf_sympy, sympykern, periodic_exponential, periodic_Matern32, periodic_Matern52, product, product_orthogonal, symmetric
+from constructors import rbf, Matern32, Matern52, exponential, linear, white, bias, finite_dimensional, spline, Brownian, rbf_sympy, sympykern, periodic_exponential, periodic_Matern32, periodic_Matern52, product, product_orthogonal, symmetric, coregionalise
 from kern import kern

GPy/kern/constructors.py

@@ -21,6 +21,7 @@ from periodic_Matern52 import periodic_Matern52 as periodic_Matern52part
 from product import product as productpart
 from product_orthogonal import product_orthogonal as product_orthogonalpart
 from symmetric import symmetric as symmetric_part
+from coregionalise import coregionalise as coregionalise_part
 #TODO these s=constructors are not as clean as we'd like. Tidy the code up
 #using meta-classes to make the objects construct properly wthout them.
 
@@ -274,3 +275,8 @@ def symmetric(k):
     k_.parts = [symmetric_part(p) for p in k.parts]
     return k_
 
+def coregionalise(Nout,R=1, W=None, kappa=None):
+    p = coregionalise_part(Nout,R,W,kappa)
+    return kern(1,[p])
+
+

GPy/kern/coregionalise.py

@@ -0,0 +1,83 @@
+# Copyright (c) 2012, James Hensman and Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+from kernpart import kernpart
+import numpy as np
+from GPy.util.linalg import mdot, pdinv
+
+class coregionalise(kernpart):
+    """
+    Kernel for Intrisec Corregionalization Models
+    """
+    def __init__(self,Nout,R=1, W=None, kappa=None):
+        self.D = 1
+        self.name = 'coregion'
+        self.Nout = Nout
+        self.R = R
+        if W is None:
+            self.W = np.ones((self.Nout,self.R))
+        else:
+            assert W.shape==(self.Nout,self.R)
+            self.W = W
+        if kappa is None:
+            kappa = np.ones(self.Nout)
+        else:
+            assert kappa.shape==(self.Nout,)
+        self.kappa = kappa
+        self.Nparam = self.Nout*(self.R + 1)
+        self._set_params(np.hstack([self.W.flatten(),self.kappa]))
+
+    def _get_params(self):
+        return np.hstack([self.W.flatten(),self.kappa])
+
+    def _set_params(self,x):
+        assert x.size == self.Nparam
+        self.kappa = x[-self.Nout:]
+        self.W = x[:-self.Nout].reshape(self.Nout,self.R)
+        self.B = np.dot(self.W,self.W.T) + np.diag(self.kappa)
+
+    def _get_param_names(self):
+
+        return sum([['W%i_%i'%(i,j) for j in range(self.R)] for i in range(self.Nout)],[]) + ['kappa_%i'%i for i in range(self.Nout)]
+
+    def K(self,index,index2,target):
+        index = np.asarray(index,dtype=np.int)
+        if index2 is None:
+            index2 = index
+        else:
+            index2 = np.asarray(index2,dtype=np.int)
+        ii,jj = np.meshgrid(index,index2)
+        target += self.B[ii,jj].T
+
+    def Kdiag(self,index,target):
+        target += np.diag(self.B)[np.asarray(index,dtype=np.int).flatten()]
+
+    def dK_dtheta(self,partial,index,index2,target):
+        index = np.asarray(index,dtype=np.int)
+        if index2 is None:
+            index2 = index
+        else:
+            index2 = np.asarray(index2,dtype=np.int)
+        ii,jj = np.meshgrid(index,index2)
+        PK = np.zeros((self.R,self.R))
+        dkappa = np.zeros(self.Nout)
+        partial_small = np.zeros_like(self.B)
+        for i in range(self.Nout):
+            for j in range(self.Nout):
+                partial_small[j,i] = np.sum(partial[(ii==i)*(jj==j)])
+        #print partial_small
+        dkappa = np.diag(partial_small)
+
+        ##target += (((X2[:, None, :] * self.variances)) * partial[:,:, None]).sum(0)
+        dW = 2.*(self.W[:,None,:]*partial_small[:,:,None]).sum(0)
+
+        target += np.hstack([dW.flatten(),dkappa])
+
+    def dKdiag_dtheta(self,partial,index,target):
+        raise NotImplementedError
+
+    def dK_dX(self,partial,X,X2,target):
+        pass
+
+
+