adding some test cases for EP.. more work needs to be done, these are some high level test cases ..

GPy/testing/inference_tests.py

@@ -61,6 +61,18 @@ class InferenceGPEP(unittest.TestCase):
         Y = lik.samples(f).reshape(-1,1)
         return X, Y
 
+    def genNoisyData(self):
+        np.random.seed(1)
+        X = np.random.rand(100,1)
+        self.real_std = 0.2
+        noise = np.random.randn(*X[:, 0].shape)*self.real_std
+        Y = (np.sin(X[:, 0]*2*np.pi) + noise)[:, None]
+        self.f = np.random.rand(X.shape[0],1)
+        Y_extra_noisy = Y.copy()
+        Y_extra_noisy[50:53] += 4.
+        Y_extra_noisy[80:83] -= 2.
+        return X, Y, Y_extra_noisy
+
     def test_inference_EP(self):
         from paramz import ObsAr
         X, Y = self.genData()
@@ -86,6 +98,39 @@ class InferenceGPEP(unittest.TestCase):
                     np.sum(p._woodbury_vector - p0._woodbury_vector),
                     np.sum(p.woodbury_inv - p0.woodbury_inv)])) < 1e6)
 
+    # NOTE: adding a test like above for parameterized likelihood- the above test is
+    # only for probit likelihood which does not have any tunable hyperparameter which is why
+    # the term in dictionary of gradients: dL_dthetaL will always be zero. So here we repeat tests for
+    # student-t likelihood and heterodescastic gaussian noise case. This test simply checks if the posterior
+    # and gradients of log marginal are roughly the same for inference through EP and exact gaussian inference using
+    # the gaussian approximation for the individual likelihood site terms. For probit likelihood, it is possible to
+    # calculate moments analytically, but for other likelihoods, we will need to use numerical quadrature techniques,
+    # and it is possible that any error might creep up because of quadrature implementation.
+    def test_inference_EP_non_classification(self):
+        from paramz import ObsAr
+        X, Y, Y_extra_noisy = self.genNoisyData()
+        deg_freedom = 5
+        init_noise_var = 0.4
+        lik_studentT = GPy.likelihoods.StudentT(deg_free=deg_freedom, sigma2=init_noise_var)
+        # like_gaussian_noise = GPy.likelihoods.MixedNoise()
+        k = GPy.kern.RBF(1, variance=2., lengthscale=1.1)
+        ep_inf_alt = GPy.inference.latent_function_inference.expectation_propagation.EP(max_iters=100, delta=0.5)
+        ep_inf_nested = GPy.inference.latent_function_inference.expectation_propagation.EP(ep_mode='nested', max_iters=100, delta=0.5)
+        m = GPy.core.GP(X=X,Y=Y_extra_noisy,kernel=k,likelihood=lik_studentT,inference_method=ep_inf_alt)
+        K = m.kern.K(X)
+        post_params, ga_approx, log_Z_tilde = m.inference_method.expectation_propagation(K, ObsAr(Y_extra_noisy), lik_studentT, None)
+
+        mu_tilde = ga_approx.v / ga_approx.tau.astype(float)
+        p, m, d = m.inference_method._inference(K, ga_approx, lik_studentT, Y_metadata=None,  Z_tilde=log_Z_tilde)
+        p0, m0, d0 = super(GPy.inference.latent_function_inference.expectation_propagation.EP, ep_inf_alt).inference(k, X,lik_studentT ,mu_tilde[:,None], mean_function=None, variance=1./ga_approx.tau, K=K, Z_tilde=log_Z_tilde + np.sum(- 0.5*np.log(ga_approx.tau) + 0.5*(ga_approx.v*ga_approx.v*1./ga_approx.tau)))
+
+        assert (np.sum(np.array([m - m0,
+                    np.sum(d['dL_dK'] - d0['dL_dK']),
+                    np.sum(d['dL_dthetaL'] - d0['dL_dthetaL']),
+                    np.sum(d['dL_dm'] - d0['dL_dm']),
+                    np.sum(p._woodbury_vector - p0._woodbury_vector),
+                    np.sum(p.woodbury_inv - p0.woodbury_inv)])) < 1e6)
+
 
 class HMCSamplerTest(unittest.TestCase):