I think the gradients bug in the sparse GP model is due to Kmm being unstable to invert. REducing M in some of the examples really helps

GPy/examples/sparse_GPLVM_demo.py

@@ -9,6 +9,7 @@ np.random.seed(1)
 print "sparse GPLVM with RBF kernel"
 
 N = 100
+M = 4
 Q = 1
 D = 2
 #generate GPLVM-like data
@@ -17,7 +18,7 @@ k = GPy.kern.rbf(Q, 1.0, 2.0) + GPy.kern.white(Q, 0.00001)
 K = k.K(X)
 Y = np.random.multivariate_normal(np.zeros(N),K,D).T
 
-m = GPy.models.sparse_GPLVM(Y, Q, M = 10)
+m = GPy.models.sparse_GPLVM(Y, Q, M=M)
 m.constrain_positive('(rbf|bias|noise)')
 m.constrain_bounded('white', 1e-3, 0.1)
 # m.plot()

GPy/examples/sparse_GP_regression_demo.py

@@ -12,6 +12,7 @@ import GPy
 np.random.seed(2)
 pb.ion()
 N = 500
+M = 5
 
 ######################################
 ## 1 dimensional example
@@ -26,7 +27,7 @@ noise = GPy.kern.white(1)
 kernel = rbf + noise
 
 # create simple GP model
-m1 = GPy.models.sparse_GP_regression(X,Y,kernel, M = 10)
+m1 = GPy.models.sparse_GP_regression(X, Y, kernel, M=M)
 
 # contrain all parameters to be positive
 m1.constrain_positive('(variance|lengthscale|precision)')

GPy/models/sparse_GP_regression.py

@@ -90,9 +90,9 @@ class sparse_GP_regression(GP_regression):
 
         # Computes dL_dKmm TODO: nicer precomputations
 
+        self.dL_dKmm = -0.5 * self.beta * self.D * mdot(self.Lmi.T, self.A, self.Lmi) # dB
         tmp = self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi)
-        self.dL_dKmm = -self.beta * self.D * 0.5 * mdot(self.Lmi.T, self.A, self.Lmi) # dB
-        self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - tmp - tmp.T + self.Kmmi) # dC
+        self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - tmp - tmp.T + self.Kmmi) # dC #TODO: is tmp PD? save some computations here
         tmp = (mdot(self.LBL_inv, self.psi1YYpsi1, self.Kmmi)
                - self.beta*mdot(self.G, self.psi2, self.Kmmi))
         self.dL_dKmm += -0.5*self.beta2*(tmp + tmp.T - self.G) # dE