Working for regression, still some bugs for EP.

GPy/examples/sparse_ep_fix.py

@@ -32,18 +32,29 @@ noise = GPy.kern.white(1)
 kernel = rbf + noise
 
 # create simple GP model
-m = GPy.models.sparse_GP(X,Y=None, kernel=kernel, M=M,likelihood= likelihood)
+#m = GPy.models.sparse_GP(X,Y=None, kernel=kernel, M=M,likelihood= likelihood)
-#m = GPy.models.sparse_GP(X, Y, kernel, M=M)
 
 # contrain all parameters to be positive
+#m.constrain_fixed('prec',100.)
+m = GPy.models.sparse_GP(X, Y, kernel, M=M)
 m.ensure_default_constraints()
-if not isinstance(m.likelihood,GPy.inference.likelihoods.gaussian):
+#if not isinstance(m.likelihood,GPy.inference.likelihoods.gaussian):
-    m.approximate_likelihood()
+#    m.approximate_likelihood()
 print m.checkgrad()
-#check gradient FIXME unit test please
+m.optimize('tnc', messages = 1)
-# optimize and plot
+m.plot(samples=3)
-#m.optimize('tnc', messages = 1)
+print m
-m.EM()
-m.plot(samples=3,full_cov=False)
-# print(m)
 
+n = GPy.models.sparse_GP(X,Y=None, kernel=kernel, M=M,likelihood= likelihood)
+n.ensure_default_constraints()
+if not isinstance(n.likelihood,GPy.inference.likelihoods.gaussian):
+    n.approximate_likelihood()
+print n.checkgrad()
+pb.figure()
+n.plot()
+
+"""
+m = GPy.models.sparse_GP_regression(X, Y, kernel, M=M)
+m.ensure_default_constraints()
+print m.checkgrad()
+"""

GPy/models/sparse_GP.py

@@ -10,6 +10,7 @@ from GP import GP
 from ..inference.EP import Full,DTC,FITC
 from ..inference.likelihoods import likelihood,probit,poisson,gaussian
 
+
 #Still TODO:
 # make use of slices properly (kernel can now do this)
 # enable heteroscedatic noise (kernel will need to compute psi2 as a (NxMxM) array)
@@ -35,12 +36,6 @@ class sparse_GP(GP):
     :type beta: float
     :param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
     :type normalize_(X|Y): bool
-    :parm likelihood: a GPy likelihood, defaults to gaussian
-    :param method_ep: sparse approximation used by Expectation Propagation algorithm, defaults to DTC
-    :type M: string (Full|DTC|FITC)
-    :param epsilon_ep: convergence criterion for the Expectation Propagation algorithm, defaults to 0.1
-    :param powerep: power-EP parameters [$\eta$,$\delta$], defaults to [1.,1.]
-    :type powerep: list
     """
 
     def __init__(self,X,Y=None,kernel=None,X_uncertainty=None,beta=100.,Z=None,Zslices=None,M=10,normalize_X=False,normalize_Y=False,likelihood=None,method_ep='DTC',epsilon_ep=1e-3,power_ep=[1.,1.]):
@@ -70,20 +65,21 @@ class sparse_GP(GP):
         else:
             self.method_ep = method_ep
 
+        #normalise X uncertainty also
+        if self.has_uncertain_inputs:
+            self.X_uncertainty /= np.square(self._Xstd)
 
     def _set_params(self, p):
         self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
         if not self.EP:
             self.beta = p[self.M*self.Q]
-            #self.beta = np.repeat(p[self.M*self.Q],self.N)[:,None]
             self.kern._set_params(p[self.Z.size + 1:])
-            self.beta2 = self.beta**2
         else:
             self.kern._set_params(p[self.Z.size:])
             if self.Y is None:
                 self.Y = np.ones([self.N,1])
         self._compute_kernel_matrices()
-        self._computations() #NOTE At this point computations of dL are not needed
+        self._computations()
 
     def _get_params(self):
         if not self.EP:
@@ -97,19 +93,22 @@ class sparse_GP(GP):
         else:
             return sum([['iip_%i_%i'%(i,j) for i in range(self.Z.shape[0])] for j in range(self.Z.shape[1])],[]) + self.kern._get_param_names_transformed()
 
+
     def _compute_kernel_matrices(self):
         # kernel computations, using BGPLVM notation
         #TODO: slices for psi statistics (easy enough)
+
         self.Kmm = self.kern.K(self.Z)
         if self.has_uncertain_inputs:
             if not self.EP:
-                self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty)#.sum()
+                self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty)#.sum() NOTE psi0 is now a vector
                 self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
-                self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)#FIXME add beta vector
+                self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)
+                #self.psi2_beta_scaled = ?
             else:
                 raise NotImplementedError, "uncertain_inputs not yet supported for EP"
         else:
-            self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices)#.sum() FIXME
+            self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices)#.sum()
             self.psi1 = self.kern.K(self.Z,self.X)
             self.psi2 = np.dot(self.psi1,self.psi1.T)
             self.psi2_beta_scaled = np.dot(self.psi1,self.beta*self.psi1.T)
@@ -124,22 +123,29 @@ class sparse_GP(GP):
         self.B = np.eye(self.M) + self.A
         self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
         self.LLambdai = np.dot(self.LBi, self.Lmi)
-        self.trace_K = self.psi0.sum() - np.trace(self.A)
         self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
         self.C = mdot(self.LLambdai, self.psi1V)
         self.G =  mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
+        self.trace_K_beta_scaled = (self.psi0*self.beta).sum() - np.trace(self.A)
+        if not self.EP:
+            self.trace_K = self.psi0.sum() - np.trace(self.A)/self.beta
 
         # Compute dL_dpsi
-        self.dL_dpsi0 = - 0.5 * self.D * self.beta.flatten() * np.ones(self.N)
         self.dL_dpsi1 = mdot(self.LLambdai.T,self.C,self.V.T)
-        #self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
+        if not self.EP:
-        self.dL_dpsi2 = - 0.5 * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
+            self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
+            if self.has_uncertain_inputs:
+                self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
+            else:
+                self.dL_dpsi2_ = - 0.5 * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
+        else:
+            self.dL_dpsi0 = - 0.5 * self.D * self.beta.flatten()
+            if not self.has_uncertain_inputs:
+                self.dL_dpsi2_ = - 0.5 * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
 
         # Compute dL_dKmm
         self.dL_dKmm = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi) # dB
-        #self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi) + self.Kmmi) # dC
         self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*mdot(self.LBL_inv, self.psi2_beta_scaled, self.Kmmi) + self.Kmmi) # dC
-        #self.dL_dKmm +=  np.dot(np.dot(self.G,self.beta*self.psi2) - np.dot(self.LBL_inv, self.psi1VVpsi1), self.Kmmi) + 0.5*self.G # dE
         self.dL_dKmm +=  np.dot(np.dot(self.G,self.psi2_beta_scaled) - np.dot(self.LBL_inv, self.psi1VVpsi1), self.Kmmi) + 0.5*self.G # dE
 
     def approximate_likelihood(self):
@@ -164,7 +170,7 @@ class sparse_GP(GP):
         else:
             A = -0.5*self.D*(self.N*np.log(2.*np.pi) - np.sum(np.log(self.beta)))
             D = -0.5*self.trbetaYYT
-        B = -0.5*self.D*self.trace_K
+        B = -0.5*self.D*self.trace_K_beta_scaled
         C = -0.5*self.D * self.B_logdet
         E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
         return A+B+C+D+E
@@ -194,7 +200,7 @@ class sparse_GP(GP):
             dL_dtheta += self.kern.dpsi2_dtheta(self.dL_dpsi2,self.Z,self.X, self.X_uncertainty) # for multiple_beta, dL_dpsi2 will be a different shape
         else:
             #re-cast computations in psi2 back to psi1:
-            dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
+            dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2_,self.beta.T*self.psi1) #dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
             dL_dtheta += self.kern.dK_dtheta(dL_dpsi1,self.Z,self.X)
             dL_dtheta += self.kern.dKdiag_dtheta(self.dL_dpsi0, self.X)
 
@@ -210,7 +216,7 @@ class sparse_GP(GP):
             dL_dZ += self.kern.dpsi2_dZ(self.dL_dpsi2,self.Z,self.X, self.X_uncertainty)
         else:
             #re-cast computations in psi2 back to psi1:
-            dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
+            dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2_,self.beta.T*self.psi1)#dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
             dL_dZ += self.kern.dK_dX(dL_dpsi1,self.Z,self.X)
         return dL_dZ
 
@@ -229,16 +235,14 @@ class sparse_GP(GP):
             Kxx = self.kern.K(Xnew)
             var = Kxx - mdot(Kx.T, (self.Kmmi - self.LBL_inv), Kx)
             if not self.EP:
-                var += np.eye(Xnew.shape[0])/self.beta # TODO: This beta doesn't belong here in the EP case.
+                var += np.eye(Xnew.shape[0])/self.beta
             else:
                 raise NotImplementedError, "full_cov = True not implemented for EP"
-                #var = np.diag(var)[:,None]
-                #phi = self.likelihood.predictive_mean(mu,var)
         else:
             Kxx = self.kern.Kdiag(Xnew)
             var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.LBL_inv, Kx),0)
             if not self.EP:
-                var += 1./self.beta # TODO: This beta doesn't belong here in the EP case.
+                var += 1./self.beta
             else:
                 phi = self.likelihood.predictive_mean(mu,var)
         return mu,var,phi
@@ -247,7 +251,6 @@ class sparse_GP(GP):
         """
         Plot the fitted model: just call the GP_regression plot function and then add inducing inputs
         """
-        #GP_regression.plot(self,*args,**kwargs)
         GP.plot(self,*args,**kwargs)
         if self.Q==1:
             pb.plot(self.Z,self.Z*0+pb.ylim()[0],'k|',mew=1.5,markersize=12)