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

GPy/testing/ep_likelihood_tests.py

@@ -0,0 +1,151 @@
+
+import numpy as np
+import unittest
+import GPy
+from GPy.models import GradientChecker
+
+import pods
+
+fixed_seed = 10
+from nose.tools import with_setup, nottest
+
+
+# this file will contain some high level tests, this is not unit testing, but will give us a higher level estimate
+# if things are going well under the hood.
+class TestObservationModels(unittest.TestCase):
+    def setUp(self):
+        np.random.seed(fixed_seed)
+        self.N = 100
+        self.D = 2
+        self.X = np.random.rand(self.N, self.D)
+
+        self.real_noise_std = 0.05
+        noise = np.random.randn(*self.X[:, 0].shape) * self.real_noise_std
+        self.Y = (np.sin(self.X[:, 0] * 2 * np.pi) + noise)[:, None]
+        self.num_points = self.X.shape[0]
+        self.f = np.random.rand(self.N, 1)
+        self.binary_Y = np.asarray(np.random.rand(self.N) > 0.5, dtype=np.int)[:, None]
+        # self.binary_Y[self.binary_Y == 0.0] = -1.0
+        self.positive_Y = np.exp(self.Y.copy())
+
+        self.Y_noisy = self.Y.copy()
+        self.Y_verynoisy = self.Y.copy()
+        self.Y_noisy[75:80] += 1.3
+
+        self.init_var = 0.3
+        self.deg_free = 5.
+        censored = np.zeros_like(self.Y)
+        random_inds = np.random.choice(self.N, int(self.N / 2), replace=True)
+        censored[random_inds] = 1
+        self.Y_metadata = dict()
+        self.Y_metadata['censored'] = censored
+        self.kernel1 = GPy.kern.RBF(self.X.shape[1]) + GPy.kern.White(self.X.shape[1])
+
+    def tearDown(self):
+        self.Y = None
+        self.X = None
+        self.binary_Y =None
+        self.positive_Y = None
+        self.kernel1 = None
+
+    @with_setup(setUp, tearDown)
+    def testEPClassification(self):
+        bernoulli = GPy.likelihoods.Bernoulli()
+        laplace_inf = GPy.inference.latent_function_inference.Laplace()
+
+        ep_inf_alt = GPy.inference.latent_function_inference.EP(ep_mode='alternated')
+        ep_inf_nested = GPy.inference.latent_function_inference.EP(ep_mode='nested')
+        ep_inf_fractional = GPy.inference.latent_function_inference.EP(ep_mode='nested', eta=0.9)
+
+        m1 = GPy.core.GP(self.X, self.binary_Y.copy(), kernel=self.kernel1.copy(), likelihood=bernoulli.copy(), inference_method=laplace_inf)
+        # m1['.*white'].constrain_fixed(1e-6)
+        # m1['.*Gaussian_noise.variance'].constrain_bounded(1e-4, 1)
+        m1.randomize()
+
+        m2 = GPy.core.GP(self.X, self.binary_Y.copy(), kernel=self.kernel1.copy(), likelihood=bernoulli.copy(), inference_method=ep_inf_alt)
+        m2.randomize()
+
+        m3 = GPy.core.GP(self.X, self.binary_Y.copy(), kernel=self.kernel1.copy(), likelihood=bernoulli.copy(), inference_method=ep_inf_nested)
+        m3.randomize()
+        #
+        m4 = GPy.core.GP(self.X, self.binary_Y.copy(), kernel=self.kernel1.copy(), likelihood=bernoulli.copy(), inference_method=ep_inf_fractional)
+        m4.randomize()
+
+        optimizer = 'bfgs'
+
+        #do gradcheck here ...
+        # self.assertTrue(m1.checkgrad())
+        # self.assertTrue(m2.checkgrad())
+        # self.assertTrue(m3.checkgrad())
+        # self.assertTrue(m4.checkgrad())
+
+        m1.optimize(optimizer=optimizer, max_iters=300)
+        m2.optimize(optimizer=optimizer, max_iters=300)
+        m3.optimize(optimizer=optimizer, max_iters=300)
+        m4.optimize(optimizer=optimizer, max_iters=300)
+
+        # taking laplace predictions as the ground truth
+        probs_mean_lap, probs_var_lap = m1.predict(self.X)
+        probs_mean_ep_alt, probs_var_ep_alt = m2.predict(self.X)
+        probs_mean_ep_nested, probs_var_ep_nested = m2.predict(self.X)
+
+        # for simple single dimension data , marginal likelihood for laplace and EP approximations should not be so far apart.
+        self.assertAlmostEqual(m1.log_likelihood(), m2.log_likelihood(),delta=1)
+        self.assertAlmostEqual(m1.log_likelihood(), m3.log_likelihood(), delta=1)
+        self.assertAlmostEqual(m1.log_likelihood(), m4.log_likelihood(), delta=5)
+
+        GPy.util.classification.conf_matrix(probs_mean_lap, self.binary_Y)
+        GPy.util.classification.conf_matrix(probs_mean_ep_alt, self.binary_Y)
+        GPy.util.classification.conf_matrix(probs_mean_ep_nested, self.binary_Y)
+
+    @nottest
+    def rmse(self, Y, Ystar):
+        return np.sqrt(np.mean((Y - Ystar) ** 2))
+
+    @with_setup(setUp, tearDown)
+    def test_EP_with_StudentT(self):
+        studentT = GPy.likelihoods.StudentT(deg_free=self.deg_free, sigma2=self.init_var)
+        laplace_inf = GPy.inference.latent_function_inference.Laplace()
+
+        ep_inf_alt = GPy.inference.latent_function_inference.EP(ep_mode='alternated')
+        ep_inf_nested = GPy.inference.latent_function_inference.EP(ep_mode='nested')
+        ep_inf_frac = GPy.inference.latent_function_inference.EP(ep_mode='nested', eta=0.7)
+
+        m1 = GPy.core.GP(self.X, self.Y_noisy.copy(), kernel=self.kernel1, likelihood=studentT.copy(), inference_method=laplace_inf)
+        # optimize
+        m1['.*white'].constrain_fixed(1e-5)
+        m1.randomize()
+
+        m2 = GPy.core.GP(self.X, self.Y_noisy.copy(), kernel=self.kernel1, likelihood=studentT.copy(), inference_method=ep_inf_alt)
+        m2['.*white'].constrain_fixed(1e-5)
+        # m2.constrain_bounded('.*t_scale2', 0.001, 10)
+        m2.randomize()
+
+        # m3 = GPy.core.GP(self.X, self.Y_noisy.copy(), kernel=self.kernel1, likelihood=studentT.copy(), inference_method=ep_inf_nested)
+        # m3['.*white'].constrain_fixed(1e-5)
+        # # m3.constrain_bounded('.*t_scale2', 0.001, 10)
+        # m3.randomize()
+
+        optimizer='bfgs'
+        m1.optimize(optimizer=optimizer,max_iters=400)
+        m2.optimize(optimizer=optimizer, max_iters=500)
+        print(m2[''])
+
+        self.assertAlmostEqual(m1.log_likelihood(), m2.log_likelihood(), 10)
+        # self.assertAlmostEqual(m1.log_likelihood(), m3.log_likelihood(), 3)
+
+        preds_mean_lap, preds_var_lap = m1.predict(self.X)
+        preds_mean_alt, preds_var_alt = m2.predict(self.X)
+        # preds_mean_nested, preds_var_nested = m3.predict(self.X)
+        rmse_lap = self.rmse(preds_mean_lap, self.Y_noisy)
+        rmse_alt = self.rmse(preds_mean_alt, self.Y_noisy)
+        # rmse_nested = self.rmse(preds_mean_nested, self.Y_noisy)
+
+        self.assertAlmostEqual(rmse_lap, rmse_alt, delta=1.)
+        # m3.optimize(optimizer=optimizer, max_iters=500)
+
+    def test_EP_with_CensoredData(self):
+        pass
+
+if __name__ == "__main__":
+    unittest.main()

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):