sparse GP regression now working on this branch

GPy/examples/sparse_GP_regression_demo.py

@@ -21,7 +21,7 @@ X = np.random.uniform(-3.,3.,(N,1))
 Y = np.sin(X)+np.random.randn(N,1)*0.05
 
 # construct kernel
-rbf =  GPy.kern.Matern52(1)
+rbf =  GPy.kern.rbf(1)
 noise = GPy.kern.white(1)
 kernel = rbf + noise
 
@@ -37,7 +37,7 @@ m1.constrain_positive('(variance|lengthscale|precision)')
 #check gradient FIXME unit test please
 m1.checkgrad()
 # optimize and plot
-m1.optimize('bfgs', messages = 1)
+m1.optimize('tnc', messages = 1)
 m1.plot()
 # print(m1)
 

GPy/kern/linear.py

@@ -48,6 +48,9 @@ class linear(kernpart):
     def dK_dX(self,partial,X,X2,target):
         target += self.variance * np.sum(partial[:,None,:]*X2.T[None,:,:],-1)
 
+    def dKdiag_dtheta(self,partial,X,target):
+        target += np.sum(partial*np.square(X).sum(1))
+
     # def psi0(self,Z,mu,S,target):
     #     expected = np.square(mu) + S
     #     np.add(target,np.sum(self.variance*expected),target)

GPy/kern/rbf.py

@@ -63,7 +63,7 @@ class rbf(kernpart):
         self._K_computations(X,X2)
         _K_dist = X[:,None,:]-X2[None,:,:]
         dK_dX = np.transpose(-self.variance*self._K_dvar[:,:,np.newaxis]*_K_dist/self.lengthscale2,(1,0,2))
-        target += np.sum(dK_dX*partial[:,:,None],0)
+        target += np.sum(dK_dX*partial.T[:,:,None],0)
 
     def dKdiag_dX(self,X,target):
         pass

GPy/kern/white.py

@@ -42,13 +42,13 @@ class white(kernpart):
             if np.all(X==X2):
                 target += np.trace(partial)
 
-    def dKdiag_dtheta(self,X,target):
-        np.add(target[:,0],1.,target[:,0])
+    def dKdiag_dtheta(self,partial,X,target):
+        target += np.sum(partial)
 
     def dK_dX(self,partial,X,X2,target):
         pass
 
-    def dKdiag_dX(self,X,target):
+    def dKdiag_dX(self,partial,X,target):
         pass
 
     def psi0(self,Z,mu,S,target):

GPy/models/sparse_GP_regression.py

@@ -63,15 +63,15 @@ class sparse_GP_regression(GP_regression):
         self.psi1 = self.kern.K(self.Z,self.X)
         self.psi2 = np.dot(self.psi1,self.psi1.T)
 
-        self.dKmm_dtheta = self.kern.dK_dtheta(self.Z)
-        self.dpsi0_dtheta = self.kern.dKdiag_dtheta(self.X).sum(0)
-        self.dpsi1_dtheta = self.kern.dK_dtheta(self.Z,self.X)
-        tmp = np.dot(self.psi1, self.dpsi1_dtheta)
-        self.dpsi2_dtheta = tmp + tmp.transpose(1,0,2)
+        #self.dKmm_dtheta = self.kern.dK_dtheta(self.Z)
+        #self.dpsi0_dtheta = self.kern.dKdiag_dtheta(self.X).sum(0)
+        #self.dpsi1_dtheta = self.kern.dK_dtheta(self.Z,self.X)
+        #tmp = np.dot(self.psi1, self.dpsi1_dtheta)
+        #self.dpsi2_dtheta = tmp + tmp.transpose(1,0,2)
 
-        self.dpsi1_dZ = self.kern.dK_dX(self.Z,self.X)
-        self.dpsi2_dZ = np.tensordot(self.psi1,self.dpsi1_dZ,((1),(0)))*2.0
-        self.dKmm_dZ = self.kern.dK_dX(self.Z)
+        #self.dpsi1_dZ = self.kern.dK_dX(self.Z,self.X)
+        #self.dpsi2_dZ = np.tensordot(self.psi1,self.dpsi1_dZ,((1),(0)))*2.0
+        #self.dKmm_dZ = self.kern.dK_dX(self.Z)
 
     def _computations(self):
         # TODO find routine to multiply triangular matrices
@@ -92,7 +92,7 @@ class sparse_GP_regression(GP_regression):
         self.G =  mdot(self.LBL_inv, self.psi1YYpsi1, self.LBL_inv.T)
 
         # Computes dL_dpsi
-        self.dL_dpsi0 = - 0.5 * self.D * self.beta
+        self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
         dC_dpsi1 = (self.LLambdai.T[:,:, None, None] * self.Y) # this is sane.
         tmp = (dC_dpsi1*self.C[None,:,None,:]).sum(1).sum(-1)
         self.dL_dpsi1 = self.beta2 * tmp
@@ -145,29 +145,34 @@ class sparse_GP_regression(GP_regression):
         return np.squeeze(dA_dbeta + dB_dbeta + dC_dbeta + dD_dbeta + dE_dbeta)
 
     def dL_dtheta(self):
-        dL_dtheta = (self.dL_dpsi0 * self.dpsi0_dtheta + (self.dL_dpsi1[:,:, None] * self.dpsi1_dtheta).sum(0).sum(0)
-                     + (self.dL_dpsi2[:, :, None] * self.dpsi2_dtheta).sum(0).sum(0)
-                     + (self.dL_dKmm[:, :, None] * self.dKmm_dtheta).sum(0).sum(0))
+        #re-cast computations in psi2 back to psi1:
+        dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
+
+        dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm,self.Z)
+        dL_dtheta += self.kern.dK_dtheta(dL_dpsi1,self.Z,self.X)
+        dL_dtheta += self.kern.dKdiag_dtheta(self.dL_dpsi0, self.X)
+
         return dL_dtheta
 
     def dL_dZ(self):
-        dL_dZ = ((self.dL_dpsi1[:,:,None]*self.dpsi1_dZ.swapaxes(0,1)).sum(1)
-                 + (self.dL_dpsi2[:, :, None] * self.dpsi2_dZ).sum(0)
-                 + 2.0*(self.dL_dKmm[:, :, None] * self.dKmm_dZ).sum(0))
-        return dL_dZ
+        #re-cast computations in psi2 back to psi1:
+        dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
 
+        dL_dZ = 2.*self.kern.dK_dX(self.dL_dKmm,self.Z,)#factor of two becase of vertical and horizontal 'stripes' in dKmm_dZ
+        dL_dZ += self.kern.dK_dX(dL_dpsi1,self.Z,self.X)
+        return dL_dZ
 
     def log_likelihood_gradients(self):
         return np.hstack([self.dL_dZ().flatten(), self.dL_dbeta(), self.dL_dtheta()])
 
-    def _raw_predict(self,_Xnew,slices):
+    def _raw_predict(self,Xnew,slices):
         """Internal helper function for making predictions, does not account for normalisation"""
 
-        Kx = self.kern.K(self.Z, _Xnew, self.Xslices, slices)
-        Kxx = self.kern.K(_Xnew, slices1=slices, slices2=slices)
+        Kx = self.kern.K(self.Z, Xnew)
+        Kxx = self.kern.K(Xnew)
 
         mu = self.beta * mdot(Kx.T, self.LBL_inv, self.psi1Y)
-        var = Kxx - mdot(Kx.T, (self.Kmmi - self.LBL_inv), Kx) + np.eye(_Xnew.shape[0])/self.beta # TODO: This beta doesn't belong here in the EP case.
+        var = Kxx - mdot(Kx.T, (self.Kmmi - self.LBL_inv), Kx) + np.eye(Xnew.shape[0])/self.beta # TODO: This beta doesn't belong here in the EP case.
         return mu,var
 
     def plot(self,*args,**kwargs):