From 1d354f5cce7e498814d4a78e7a0202bc90ea44bc Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Fri, 11 Sep 2015 15:08:30 +0100
Subject: [PATCH 01/22] [classification] sparse gp classification and dtc
 update

---
 GPy/core/sparse_gp.py                         |   5 +-
 GPy/examples/classification.py                |  47 ++-
 .../expectation_propagation.py                |   7 +-
 .../expectation_propagation_dtc.py            | 302 +++---------------
 .../latent_function_inference/var_dtc.py      |  40 +--
 GPy/likelihoods/bernoulli.py                  |   3 +-
 GPy/models/__init__.py                        |   4 +-
 GPy/models/bayesian_gplvm_minibatch.py        |   5 -
 GPy/models/sparse_gp_classification.py        |  59 +++-
 GPy/models/sparse_gp_minibatch.py             |   9 +-
 GPy/models/sparse_gp_regression.py            |  49 +--
 GPy/plotting/matplot_dep/models_plots.py      |  21 +-
 GPy/testing/model_tests.py                    |  21 +-
 setup.py                                      |   5 +-
 14 files changed, 208 insertions(+), 369 deletions(-)

diff --git a/GPy/core/sparse_gp.py b/GPy/core/sparse_gp.py
index d03ebd5a..56400d91 100644
--- a/GPy/core/sparse_gp.py
+++ b/GPy/core/sparse_gp.py
@@ -40,7 +40,7 @@ class SparseGP(GP):
 
     """
 
-    def __init__(self, X, Y, Z, kernel, likelihood, mean_function=None, inference_method=None,
+    def __init__(self, X, Y, Z, kernel, likelihood, mean_function=None, X_variance=None, inference_method=None,
                  name='sparse gp', Y_metadata=None, normalizer=False):
         #pick a sensible inference method
         if inference_method is None:
@@ -73,11 +73,12 @@ class SparseGP(GP):
         self.Z = Param('inducing inputs',Z)
         self.link_parameter(self.Z, index=0)
         if trigger_update: self.update_model(True)
-        if trigger_update: self._trigger_params_changed()
 
     def parameters_changed(self):
         self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.Z, self.likelihood, self.Y, self.Y_metadata)
+        self._update_gradients()
 
+    def _update_gradients(self):
         self.likelihood.update_gradients(self.grad_dict['dL_dthetaL'])
 
         if isinstance(self.X, VariationalPosterior):
diff --git a/GPy/examples/classification.py b/GPy/examples/classification.py
index 3aa022e0..ae4e9ba3 100644
--- a/GPy/examples/classification.py
+++ b/GPy/examples/classification.py
@@ -15,7 +15,7 @@ def oil(num_inducing=50, max_iters=100, kernel=None, optimize=True, plot=True):
 
     """
     try:import pods
-    except ImportError:print('pods unavailable, see https://github.com/sods/ods for example datasets')
+    except ImportError:raise ImportWarning('Need pods for example datasets. See https://github.com/sods/ods, or pip install pods.')
     data = pods.datasets.oil()
     X = data['X']
     Xtest = data['Xtest']
@@ -26,6 +26,7 @@ def oil(num_inducing=50, max_iters=100, kernel=None, optimize=True, plot=True):
 
     # Create GP model
     m = GPy.models.SparseGPClassification(X, Y, kernel=kernel, num_inducing=num_inducing)
+    m.Ytest = Ytest
 
     # Contrain all parameters to be positive
     #m.tie_params('.*len')
@@ -33,8 +34,7 @@ def oil(num_inducing=50, max_iters=100, kernel=None, optimize=True, plot=True):
 
     # Optimize
     if optimize:
-        for _ in range(5):
-            m.optimize(max_iters=int(max_iters/5))
+        m.optimize(messages=1)
     print(m)
 
     #Test
@@ -50,9 +50,8 @@ def toy_linear_1d_classification(seed=default_seed, optimize=True, plot=True):
     :type seed: int
 
     """
-
     try:import pods
-    except ImportError:print('pods unavailable, see https://github.com/sods/ods for example datasets')
+    except ImportError:raise ImportWarning('Need pods for example datasets. See https://github.com/sods/ods, or pip install pods.')
     data = pods.datasets.toy_linear_1d_classification(seed=seed)
     Y = data['Y'][:, 0:1]
     Y[Y.flatten() == -1] = 0
@@ -150,6 +149,42 @@ def sparse_toy_linear_1d_classification(num_inducing=10, seed=default_seed, opti
     print(m)
     return m
 
+def sparse_toy_linear_1d_classification_uncertain_input(num_inducing=10, seed=default_seed, optimize=True, plot=True):
+    """
+    Sparse 1D classification example
+
+    :param seed: seed value for data generation (default is 4).
+    :type seed: int
+
+    """
+
+    try:import pods
+    except ImportError:print('pods unavailable, see https://github.com/sods/ods for example datasets')
+    import numpy as np
+    data = pods.datasets.toy_linear_1d_classification(seed=seed)
+    Y = data['Y'][:, 0:1]
+    Y[Y.flatten() == -1] = 0
+    X = data['X']
+    X_var = np.random.uniform(0.3,0.5,X.shape)
+
+    # Model definition
+    m = GPy.models.SparseGPClassificationUncertainInput(X, X_var, Y, num_inducing=num_inducing)
+    m['.*len'] = 4.
+
+    # Optimize
+    if optimize:
+        m.optimize()
+
+    # Plot
+    if plot:
+        from matplotlib import pyplot as plt
+        fig, axes = plt.subplots(2, 1)
+        m.plot_f(ax=axes[0])
+        m.plot(ax=axes[1])
+
+    print(m)
+    return m
+
 def toy_heaviside(seed=default_seed, max_iters=100, optimize=True, plot=True):
     """
     Simple 1D classification example using a heavy side gp transformation
@@ -218,7 +253,7 @@ def crescent_data(model_type='Full', num_inducing=10, seed=default_seed, kernel=
         m = GPy.models.FITCClassification(data['X'], Y, kernel=kernel, num_inducing=num_inducing)
         m['.*len'] = 3.
     if optimize:
-        m.optimize()
+        m.optimize(messages=1)
 
     if plot:
         m.plot()
diff --git a/GPy/inference/latent_function_inference/expectation_propagation.py b/GPy/inference/latent_function_inference/expectation_propagation.py
index 85841a33..f621dcc7 100644
--- a/GPy/inference/latent_function_inference/expectation_propagation.py
+++ b/GPy/inference/latent_function_inference/expectation_propagation.py
@@ -4,6 +4,7 @@ import numpy as np
 from ...util.linalg import pdinv,jitchol,DSYR,tdot,dtrtrs, dpotrs
 from .posterior import Posterior
 from . import LatentFunctionInference
+from ...util import diag
 log_2_pi = np.log(2*np.pi)
 
 class EP(LatentFunctionInference):
@@ -41,7 +42,6 @@ class EP(LatentFunctionInference):
         K = kern.K(X)
 
         if self._ep_approximation is None:
-
             #if we don't yet have the results of runnign EP, run EP and store the computed factors in self._ep_approximation
             mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation = self.expectation_propagation(K, Y, likelihood, Y_metadata)
         else:
@@ -69,6 +69,7 @@ class EP(LatentFunctionInference):
         #Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma)
         mu = np.zeros(num_data)
         Sigma = K.copy()
+        diag.add(Sigma, 1e-7)
 
         #Initial values - Marginal moments
         Z_hat = np.empty(num_data,dtype=np.float64)
@@ -79,14 +80,14 @@ class EP(LatentFunctionInference):
         if self.old_mutilde is None:
             tau_tilde, mu_tilde, v_tilde = np.zeros((3, num_data))
         else:
-            assert old_mutilde.size == num_data, "data size mis-match: did you change the data? try resetting!"
+            assert self.old_mutilde.size == num_data, "data size mis-match: did you change the data? try resetting!"
             mu_tilde, v_tilde = self.old_mutilde, self.old_vtilde
             tau_tilde = v_tilde/mu_tilde
 
         #Approximation
         tau_diff = self.epsilon + 1.
         v_diff = self.epsilon + 1.
-       	iterations = 0
+        iterations = 0
         while (tau_diff > self.epsilon) or (v_diff > self.epsilon):
             update_order = np.random.permutation(num_data)
             for i in update_order:
diff --git a/GPy/inference/latent_function_inference/expectation_propagation_dtc.py b/GPy/inference/latent_function_inference/expectation_propagation_dtc.py
index e182c9f7..af71f395 100644
--- a/GPy/inference/latent_function_inference/expectation_propagation_dtc.py
+++ b/GPy/inference/latent_function_inference/expectation_propagation_dtc.py
@@ -3,27 +3,18 @@
 
 import numpy as np
 from ...util import diag
-from ...util.linalg import mdot, jitchol, backsub_both_sides, tdot, dtrtrs, dtrtri, dpotri, dpotrs, symmetrify, DSYR
-from ...core.parameterization.variational import VariationalPosterior
-from . import LatentFunctionInference
-from .posterior import Posterior
+from ...util.linalg import jitchol, dtrtrs, dtrtri, DSYR
+from ...core.parameterization.observable_array import ObsAr
+from . import VarDTC
 log_2_pi = np.log(2*np.pi)
 
-class EPDTC(LatentFunctionInference):
+class EPDTC(VarDTC):
     const_jitter = 1e-6
     def __init__(self, epsilon=1e-6, eta=1., delta=1., limit=1):
-        from ...util.caching import Cacher
-        self.limit = limit
-        self.get_trYYT = Cacher(self._get_trYYT, limit)
-        self.get_YYTfactor = Cacher(self._get_YYTfactor, limit)
-
+        super(EPDTC, self).__init__(limit=limit)
         self.epsilon, self.eta, self.delta = epsilon, eta, delta
         self.reset()
 
-    def set_limit(self, limit):
-        self.get_trYYT.limit = limit
-        self.get_YYTfactor.limit = limit
-
     def on_optimization_start(self):
         self._ep_approximation = None
 
@@ -31,212 +22,74 @@ class EPDTC(LatentFunctionInference):
         # TODO: update approximation in the end as well? Maybe even with a switch?
         pass
 
-    def _get_trYYT(self, Y):
-        return np.sum(np.square(Y))
-
-    def __getstate__(self):
-        # has to be overridden, as Cacher objects cannot be pickled.
-        return self.limit
-
-    def __setstate__(self, state):
-        # has to be overridden, as Cacher objects cannot be pickled.
-        self.limit = state
-        from ...util.caching import Cacher
-        self.get_trYYT = Cacher(self._get_trYYT, self.limit)
-        self.get_YYTfactor = Cacher(self._get_YYTfactor, self.limit)
-
-    def _get_YYTfactor(self, Y):
-        """
-        find a matrix L which satisfies LLT = YYT.
-
-        Note that L may have fewer columns than Y.
-        """
-        N, D = Y.shape
-        if (N>=D):
-            return Y
-        else:
-            return jitchol(tdot(Y))
-
-    def get_VVTfactor(self, Y, prec):
-        return Y * prec # TODO chache this, and make it effective
-
     def reset(self):
         self.old_mutilde, self.old_vtilde = None, None
         self._ep_approximation = None
 
-    def inference(self, kern, X, Z, likelihood, Y, mean_function=None, Y_metadata=None):
-        assert mean_function is None, "inference with a mean function not implemented"
-        num_data, output_dim = Y.shape
-        assert output_dim ==1, "ep in 1D only (for now!)"
+    def inference(self, kern, X, Z, likelihood, Y, mean_function=None, Y_metadata=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
+        assert Y.shape[1]==1, "ep in 1D only (for now!)"
 
         Kmm = kern.K(Z)
-        Kmn = kern.K(Z,X)
+        if psi1 is None:
+            try:
+                Kmn = kern.K(Z, X)
+            except TypeError:
+                Kmn = kern.psi1(Z, X).T
+        else:
+            Kmn = psi1.T
 
         if self._ep_approximation is None:
             mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation = self.expectation_propagation(Kmm, Kmn, Y, likelihood, Y_metadata)
         else:
             mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation
 
-
-        if isinstance(X, VariationalPosterior):
-            uncertain_inputs = True
-            psi0 = kern.psi0(Z, X)
-            psi1 = Kmn.T#kern.psi1(Z, X)
-            psi2 = kern.psi2(Z, X)
-        else:
-            uncertain_inputs = False
-            psi0 = kern.Kdiag(X)
-            psi1 = Kmn.T#kern.K(X, Z)
-            psi2 = None
-
-        #see whether we're using variational uncertain inputs
-
-        _, output_dim = Y.shape
-
-        #see whether we've got a different noise variance for each datum
-        #beta = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), 1e-6)
-        beta = tau_tilde
-        VVT_factor = beta[:,None]*mu_tilde[:,None]
-        trYYT = self.get_trYYT(mu_tilde[:,None])
-
-        # do the inference:
-        het_noise = beta.size > 1
-        num_inducing = Z.shape[0]
-        num_data = Y.shape[0]
-        # kernel computations, using BGPLVM notation
-
-        Kmm = kern.K(Z).copy()
-        diag.add(Kmm, self.const_jitter)
-        Lm = jitchol(Kmm)
-
-        # The rather complex computations of A
-        if uncertain_inputs:
-            if het_noise:
-                psi2_beta = psi2 * (beta.flatten().reshape(num_data, 1, 1)).sum(0)
-            else:
-                psi2_beta = psi2.sum(0) * beta
-            LmInv = dtrtri(Lm)
-            A = LmInv.dot(psi2_beta.dot(LmInv.T))
-        else:
-            if het_noise:
-                tmp = psi1 * (np.sqrt(beta.reshape(num_data, 1)))
-            else:
-                tmp = psi1 * (np.sqrt(beta))
-            tmp, _ = dtrtrs(Lm, tmp.T, lower=1)
-            A = tdot(tmp) #print A.sum()
-
-        # factor B
-        B = np.eye(num_inducing) + A
-        LB = jitchol(B)
-        psi1Vf = np.dot(psi1.T, VVT_factor)
-        # back substutue C into psi1Vf
-        tmp, _ = dtrtrs(Lm, psi1Vf, lower=1, trans=0)
-        _LBi_Lmi_psi1Vf, _ = dtrtrs(LB, tmp, lower=1, trans=0)
-        tmp, _ = dtrtrs(LB, _LBi_Lmi_psi1Vf, lower=1, trans=1)
-        Cpsi1Vf, _ = dtrtrs(Lm, tmp, lower=1, trans=1)
-
-        # data fit and derivative of L w.r.t. Kmm
-        delit = tdot(_LBi_Lmi_psi1Vf)
-        data_fit = np.trace(delit)
-        DBi_plus_BiPBi = backsub_both_sides(LB, output_dim * np.eye(num_inducing) + delit)
-        delit = -0.5 * DBi_plus_BiPBi
-        delit += -0.5 * B * output_dim
-        delit += output_dim * np.eye(num_inducing)
-        # Compute dL_dKmm
-        dL_dKmm = backsub_both_sides(Lm, delit)
-
-        # derivatives of L w.r.t. psi
-        dL_dpsi0, dL_dpsi1, dL_dpsi2 = _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm,
-            VVT_factor, Cpsi1Vf, DBi_plus_BiPBi,
-            psi1, het_noise, uncertain_inputs)
-
-        # log marginal likelihood
-        log_marginal = _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise,
-            psi0, A, LB, trYYT, data_fit, VVT_factor)
-
-        #put the gradients in the right places
-        dL_dR = _compute_dL_dR(likelihood,
-            het_noise, uncertain_inputs, LB,
-            _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A,
-            psi0, psi1, beta,
-            data_fit, num_data, output_dim, trYYT, mu_tilde[:,None])
-
-        dL_dthetaL = 0#likelihood.exact_inference_gradients(dL_dR,Y_metadata)
-
-        if uncertain_inputs:
-            grad_dict = {'dL_dKmm': dL_dKmm,
-                         'dL_dpsi0':dL_dpsi0,
-                         'dL_dpsi1':dL_dpsi1,
-                         'dL_dpsi2':dL_dpsi2,
-                         'dL_dthetaL':dL_dthetaL}
-        else:
-            grad_dict = {'dL_dKmm': dL_dKmm,
-                         'dL_dKdiag':dL_dpsi0,
-                         'dL_dKnm':dL_dpsi1,
-                         'dL_dthetaL':dL_dthetaL}
-
-        #get sufficient things for posterior prediction
-        #TODO: do we really want to do this in  the loop?
-        if VVT_factor.shape[1] == Y.shape[1]:
-            woodbury_vector = Cpsi1Vf # == Cpsi1V
-        else:
-            print('foobar')
-            psi1V = np.dot(mu_tilde[:,None].T*beta, psi1).T
-            tmp, _ = dtrtrs(Lm, psi1V, lower=1, trans=0)
-            tmp, _ = dpotrs(LB, tmp, lower=1)
-            woodbury_vector, _ = dtrtrs(Lm, tmp, lower=1, trans=1)
-        Bi, _ = dpotri(LB, lower=1)
-        symmetrify(Bi)
-        Bi = -dpotri(LB, lower=1)[0]
-        diag.add(Bi, 1)
-
-        woodbury_inv = backsub_both_sides(Lm, Bi)
-
-        #construct a posterior object
-        post = Posterior(woodbury_inv=woodbury_inv, woodbury_vector=woodbury_vector, K=Kmm, mean=None, cov=None, K_chol=Lm)
-        return post, log_marginal, grad_dict
-
-
-
-
+        return super(EPDTC, self).inference(kern, X, Z, likelihood, mu_tilde,
+                                            mean_function=mean_function,
+                                            Y_metadata=Y_metadata,
+                                            beta=tau_tilde,
+                                            Lm=Lm, dL_dKmm=dL_dKmm,
+                                            psi0=psi0, psi1=psi1, psi2=psi2)
 
     def expectation_propagation(self, Kmm, Kmn, Y, likelihood, Y_metadata):
+        num_data, output_dim = Y.shape
+        assert output_dim == 1, "This EP methods only works for 1D outputs"
 
-        num_data, data_dim = Y.shape
-        assert data_dim == 1, "This EP methods only works for 1D outputs"
+        LLT0 = Kmm.copy()
+        #diag.add(LLT0, 1e-8)
 
-        KmnKnm = np.dot(Kmn,Kmn.T)
-        Lm = jitchol(Kmm)
-        Lmi = dtrtrs(Lm,np.eye(Lm.shape[0]))[0] #chol_inv(Lm)
+        Lm = jitchol(LLT0)
+        Lmi = dtrtri(Lm)
         Kmmi = np.dot(Lmi.T,Lmi)
         KmmiKmn = np.dot(Kmmi,Kmn)
         Qnn_diag = np.sum(Kmn*KmmiKmn,-2)
-        LLT0 = Kmm.copy()
 
         #Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma)
         mu = np.zeros(num_data)
         LLT = Kmm.copy() #Sigma = K.copy()
-        Sigma_diag = Qnn_diag.copy()
+        Sigma_diag = Qnn_diag.copy() + 1e-8
 
         #Initial values - Marginal moments
-        Z_hat = np.empty(num_data,dtype=np.float64)
-        mu_hat = np.empty(num_data,dtype=np.float64)
-        sigma2_hat = np.empty(num_data,dtype=np.float64)
+        Z_hat = np.zeros(num_data,dtype=np.float64)
+        mu_hat = np.zeros(num_data,dtype=np.float64)
+        sigma2_hat = np.zeros(num_data,dtype=np.float64)
 
         #initial values - Gaussian factors
         if self.old_mutilde is None:
             tau_tilde, mu_tilde, v_tilde = np.zeros((3, num_data))
         else:
-            assert old_mutilde.size == num_data, "data size mis-match: did you change the data? try resetting!"
+            assert self.old_mutilde.size == num_data, "data size mis-match: did you change the data? try resetting!"
             mu_tilde, v_tilde = self.old_mutilde, self.old_vtilde
             tau_tilde = v_tilde/mu_tilde
 
         #Approximation
         tau_diff = self.epsilon + 1.
         v_diff = self.epsilon + 1.
-       	iterations = 0
+        iterations = 0
+        tau_tilde_old = 0.
+        v_tilde_old = 0.
+        update_order = np.random.permutation(num_data)
+
         while (tau_diff > self.epsilon) or (v_diff > self.epsilon):
-            update_order = np.random.permutation(num_data)
             for i in update_order:
                 #Cavity distribution parameters
                 tau_cav = 1./Sigma_diag[i] - self.eta*tau_tilde[i]
@@ -252,7 +105,7 @@ class EPDTC(LatentFunctionInference):
 
                 #DSYR(Sigma, Sigma[:,i].copy(), -delta_tau/(1.+ delta_tau*Sigma[i,i]))
                 DSYR(LLT,Kmn[:,i].copy(),delta_tau)
-                L = jitchol(LLT)
+                L = jitchol(LLT+np.eye(LLT.shape[0])*1e-7)
 
                 V,info = dtrtrs(L,Kmn,lower=1)
                 Sigma_diag = np.sum(V*V,-2)
@@ -262,9 +115,10 @@ class EPDTC(LatentFunctionInference):
 
             #(re) compute Sigma and mu using full Cholesky decompy
             LLT = LLT0 + np.dot(Kmn*tau_tilde[None,:],Kmn.T)
+            #diag.add(LLT, 1e-8)
             L = jitchol(LLT)
-            V,info = dtrtrs(L,Kmn,lower=1)
-            V2,info = dtrtrs(L.T,V,lower=0)
+            V, _ = dtrtrs(L,Kmn,lower=1)
+            V2, _ = dtrtrs(L.T,V,lower=0)
             #Sigma_diag = np.sum(V*V,-2)
             #Knmv_tilde = np.dot(Kmn,v_tilde)
             #mu = np.dot(V2.T,Knmv_tilde)
@@ -272,81 +126,17 @@ class EPDTC(LatentFunctionInference):
             mu = np.dot(Sigma,v_tilde)
 
             #monitor convergence
-            if iterations>0:
-                tau_diff = np.mean(np.square(tau_tilde-tau_tilde_old))
-                v_diff = np.mean(np.square(v_tilde-v_tilde_old))
+            #if iterations>0:
+            tau_diff = np.mean(np.square(tau_tilde-tau_tilde_old))
+            v_diff = np.mean(np.square(v_tilde-v_tilde_old))
+
             tau_tilde_old = tau_tilde.copy()
             v_tilde_old = v_tilde.copy()
 
+            # Only to while loop once:?
             tau_diff = 0
             v_diff = 0
             iterations += 1
 
         mu_tilde = v_tilde/tau_tilde
-        return mu, Sigma, mu_tilde, tau_tilde, Z_hat
-
-def _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm, VVT_factor, Cpsi1Vf, DBi_plus_BiPBi, psi1, het_noise, uncertain_inputs):
-    dL_dpsi0 = -0.5 * output_dim * (beta[:,None] * np.ones([num_data, 1])).flatten()
-    dL_dpsi1 = np.dot(VVT_factor, Cpsi1Vf.T)
-    dL_dpsi2_beta = 0.5 * backsub_both_sides(Lm, output_dim * np.eye(num_inducing) - DBi_plus_BiPBi)
-    if het_noise:
-        if uncertain_inputs:
-            dL_dpsi2 = beta[:, None, None] * dL_dpsi2_beta[None, :, :]
-        else:
-            dL_dpsi1 += 2.*np.dot(dL_dpsi2_beta, (psi1 * beta.reshape(num_data, 1)).T).T
-            dL_dpsi2 = None
-    else:
-        dL_dpsi2 = beta * dL_dpsi2_beta
-        if uncertain_inputs:
-            # repeat for each of the N psi_2 matrices
-            dL_dpsi2 = np.repeat(dL_dpsi2[None, :, :], num_data, axis=0)
-        else:
-            # subsume back into psi1 (==Kmn)
-            dL_dpsi1 += 2.*np.dot(psi1, dL_dpsi2)
-            dL_dpsi2 = None
-
-    return dL_dpsi0, dL_dpsi1, dL_dpsi2
-
-
-def _compute_dL_dR(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A, psi0, psi1, beta, data_fit, num_data, output_dim, trYYT, Y):
-    # the partial derivative vector for the likelihood
-    if likelihood.size == 0:
-        # save computation here.
-        dL_dR = None
-    elif het_noise:
-        if uncertain_inputs:
-            raise NotImplementedError("heteroscedatic derivates with uncertain inputs not implemented")
-        else:
-            #from ...util.linalg import chol_inv
-            #LBi = chol_inv(LB)
-            LBi, _ = dtrtrs(LB,np.eye(LB.shape[0]))
-
-            Lmi_psi1, nil = dtrtrs(Lm, psi1.T, lower=1, trans=0)
-            _LBi_Lmi_psi1, _ = dtrtrs(LB, Lmi_psi1, lower=1, trans=0)
-
-            dL_dR = -0.5 * beta + 0.5 * (beta*Y)**2
-            dL_dR += 0.5 * output_dim * (psi0 - np.sum(Lmi_psi1**2,0))[:,None] * beta**2
-
-            dL_dR += 0.5*np.sum(mdot(LBi.T,LBi,Lmi_psi1)*Lmi_psi1,0)[:,None]*beta**2
-
-            dL_dR += -np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T * Y * beta**2
-            dL_dR += 0.5*np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T**2 * beta**2
-    else:
-        # likelihood is not heteroscedatic
-        dL_dR = -0.5 * num_data * output_dim * beta + 0.5 * trYYT * beta ** 2
-        dL_dR += 0.5 * output_dim * (psi0.sum() * beta ** 2 - np.trace(A) * beta)
-        dL_dR += beta * (0.5 * np.sum(A * DBi_plus_BiPBi) - data_fit)
-    return dL_dR
-
-def _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise, psi0, A, LB, trYYT, data_fit,Y):
-    #compute log marginal likelihood
-    if het_noise:
-        lik_1 = -0.5 * num_data * output_dim * np.log(2. * np.pi) + 0.5 * np.sum(np.log(beta)) - 0.5 * np.sum(beta * np.square(Y).sum(axis=-1))
-        lik_2 = -0.5 * output_dim * (np.sum(beta.flatten() * psi0) - np.trace(A))
-    else:
-        lik_1 = -0.5 * num_data * output_dim * (np.log(2. * np.pi) - np.log(beta)) - 0.5 * beta * trYYT
-        lik_2 = -0.5 * output_dim * (np.sum(beta * psi0) - np.trace(A))
-    lik_3 = -output_dim * (np.sum(np.log(np.diag(LB))))
-    lik_4 = 0.5 * data_fit
-    log_marginal = lik_1 + lik_2 + lik_3 + lik_4
-    return log_marginal
+        return mu, Sigma, ObsAr(mu_tilde[:,None]), tau_tilde, Z_hat
diff --git a/GPy/inference/latent_function_inference/var_dtc.py b/GPy/inference/latent_function_inference/var_dtc.py
index e50daa24..f46d91f1 100644
--- a/GPy/inference/latent_function_inference/var_dtc.py
+++ b/GPy/inference/latent_function_inference/var_dtc.py
@@ -64,31 +64,30 @@ class VarDTC(LatentFunctionInference):
     def get_VVTfactor(self, Y, prec):
         return Y * prec # TODO chache this, and make it effective
 
-    def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
+    def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None, mean_function=None, beta=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
+        assert mean_function is None, "inference with a mean function not implemented"
+
+        num_data, output_dim = Y.shape
+        num_inducing = Z.shape[0]
 
-        _, output_dim = Y.shape
         uncertain_inputs = isinstance(X, VariationalPosterior)
 
-        #see whether we've got a different noise variance for each datum
-        beta = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), 1e-6)
-        # VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency!
-        #self.YYTfactor = self.get_YYTfactor(Y)
-        #VVT_factor = self.get_VVTfactor(self.YYTfactor, beta)
-        het_noise = beta.size > 1
+        if beta is None:
+            #assume Gaussian likelihood
+            beta = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), self.const_jitter)
+
         if beta.ndim == 1:
             beta = beta[:, None]
+        het_noise = beta.size > 1
+
         VVT_factor = beta*Y
         #VVT_factor = beta*Y
         trYYT = self.get_trYYT(Y)
 
-        # do the inference:
-        num_inducing = Z.shape[0]
-        num_data = Y.shape[0]
         # kernel computations, using BGPLVM notation
-
-        Kmm = kern.K(Z).copy()
-        diag.add(Kmm, self.const_jitter)
         if Lm is None:
+            Kmm = kern.K(Z).copy()
+            diag.add(Kmm, self.const_jitter)
             Lm = jitchol(Kmm)
 
         # The rather complex computations of A, and the psi stats
@@ -99,15 +98,16 @@ class VarDTC(LatentFunctionInference):
                 psi1 = kern.psi1(Z, X)
             if het_noise:
                 if psi2 is None:
-                    assert len(psi2.shape) == 3  # Need to have not summed out N
-                    #FIXME: Need testing
-                    psi2_beta = np.sum([psi2[X[i:i+1,:], :, :] * beta_i for i,beta_i in enumerate(beta)],0)
+                    psi2_beta = (kern.psi2n(Z, X) * beta[:, :, None]).sum(0)
                 else:
-                    psi2_beta = np.sum([kern.psi2(Z,X[i:i+1,:]) * beta_i for i,beta_i in enumerate(beta)],0)
+                    psi2_beta = (psi2 * beta[:, :, None]).sum(0)
             else:
                 if psi2 is None:
-                    psi2 = kern.psi2(Z,X)
-                psi2_beta =  psi2 * beta
+                    psi2_beta = kern.psi2(Z,X) * beta
+                elif psi2.ndim == 3:
+                    psi2_beta = psi2.sum(0) * beta
+                else:
+                    psi2_beta = psi2 * beta
             LmInv = dtrtri(Lm)
             A = LmInv.dot(psi2_beta.dot(LmInv.T))
         else:
diff --git a/GPy/likelihoods/bernoulli.py b/GPy/likelihoods/bernoulli.py
index 167daee8..1c55a89a 100644
--- a/GPy/likelihoods/bernoulli.py
+++ b/GPy/likelihoods/bernoulli.py
@@ -60,13 +60,14 @@ class Bernoulli(Likelihood):
         if isinstance(self.gp_link, link_functions.Probit):
             z = sign*v_i/np.sqrt(tau_i**2 + tau_i)
             Z_hat = std_norm_cdf(z)
+            Z_hat = np.where(Z_hat==0, 1e-15, Z_hat)
             phi = std_norm_pdf(z)
             mu_hat = v_i/tau_i + sign*phi/(Z_hat*np.sqrt(tau_i**2 + tau_i))
             sigma2_hat = 1./tau_i - (phi/((tau_i**2+tau_i)*Z_hat))*(z+phi/Z_hat)
 
         elif isinstance(self.gp_link, link_functions.Heaviside):
             a = sign*v_i/np.sqrt(tau_i)
-            Z_hat = std_norm_cdf(a)
+            Z_hat = np.max(1e-13, std_norm_cdf(z))
             N = std_norm_pdf(a)
             mu_hat = v_i/tau_i + sign*N/Z_hat/np.sqrt(tau_i)
             sigma2_hat = (1. - a*N/Z_hat - np.square(N/Z_hat))/tau_i
diff --git a/GPy/models/__init__.py b/GPy/models/__init__.py
index f01390e4..4d645bea 100644
--- a/GPy/models/__init__.py
+++ b/GPy/models/__init__.py
@@ -3,8 +3,8 @@
 
 from .gp_regression import GPRegression
 from .gp_classification import GPClassification
-from .sparse_gp_regression import SparseGPRegression, SparseGPRegressionUncertainInput
-from .sparse_gp_classification import SparseGPClassification
+from .sparse_gp_regression import SparseGPRegression
+from .sparse_gp_classification import SparseGPClassification, SparseGPClassificationUncertainInput
 from .gplvm import GPLVM
 from .bcgplvm import BCGPLVM
 from .sparse_gplvm import SparseGPLVM
diff --git a/GPy/models/bayesian_gplvm_minibatch.py b/GPy/models/bayesian_gplvm_minibatch.py
index 0394ff7e..175c3e56 100644
--- a/GPy/models/bayesian_gplvm_minibatch.py
+++ b/GPy/models/bayesian_gplvm_minibatch.py
@@ -81,11 +81,6 @@ class BayesianGPLVMMiniBatch(SparseGPMiniBatch):
         """Get the gradients of the posterior distribution of X in its specific form."""
         return X.mean.gradient, X.variance.gradient
 
-    def _inner_parameters_changed(self, kern, X, Z, likelihood, Y, Y_metadata, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None, **kw):
-        posterior, log_marginal_likelihood, grad_dict = super(BayesianGPLVMMiniBatch, self)._inner_parameters_changed(kern, X, Z, likelihood, Y, Y_metadata, Lm=Lm, dL_dKmm=dL_dKmm,
-                                                                                                                    psi0=psi0, psi1=psi1, psi2=psi2, **kw)
-        return posterior, log_marginal_likelihood, grad_dict
-
     def _outer_values_update(self, full_values):
         """
         Here you put the values, which were collected before in the right places.
diff --git a/GPy/models/sparse_gp_classification.py b/GPy/models/sparse_gp_classification.py
index e281a4b9..a3e43cf8 100644
--- a/GPy/models/sparse_gp_classification.py
+++ b/GPy/models/sparse_gp_classification.py
@@ -11,7 +11,7 @@ from ..inference.latent_function_inference import expectation_propagation_dtc
 
 class SparseGPClassification(SparseGP):
     """
-    sparse Gaussian Process model for classification
+    Sparse Gaussian Process model for classification
 
     This is a thin wrapper around the sparse_GP class, with a set of sensible defaults
 
@@ -27,10 +27,7 @@ class SparseGPClassification(SparseGP):
 
     """
 
-    #def __init__(self, X, Y=None, likelihood=None, kernel=None, normalize_X=False, normalize_Y=False, Z=None, num_inducing=10):
     def __init__(self, X, Y=None, likelihood=None, kernel=None, Z=None, num_inducing=10, Y_metadata=None):
-
-
         if kernel is None:
             kernel = kern.RBF(X.shape[1])
 
@@ -43,4 +40,56 @@ class SparseGPClassification(SparseGP):
             assert Z.shape[1] == X.shape[1]
 
         SparseGP.__init__(self, X, Y, Z, kernel, likelihood, inference_method=expectation_propagation_dtc.EPDTC(), name='SparseGPClassification',Y_metadata=Y_metadata)
-    #def __init__(self, X, Y, Z, kernel, likelihood, inference_method=None, name='sparse gp', Y_metadata=None):
+
+class SparseGPClassificationUncertainInput(SparseGP):
+    """
+    Sparse Gaussian Process model for classification with uncertain inputs.
+
+    This is a thin wrapper around the sparse_GP class, with a set of sensible defaults
+
+    :param X: input observations
+    :type X: np.ndarray (num_data x input_dim)
+    :param X_variance: The uncertainty in the measurements of X (Gaussian variance, optional)
+    :type X_variance: np.ndarray (num_data x input_dim)
+    :param Y: observed values
+    :param kernel: a GPy kernel, defaults to rbf+white
+    :param Z: inducing inputs (optional, see note)
+    :type Z: np.ndarray (num_inducing x input_dim) | None
+    :param num_inducing: number of inducing points (ignored if Z is passed, see note)
+    :type num_inducing: int
+    :rtype: model object
+
+    .. Note:: If no Z array is passed, num_inducing (default 10) points are selected from the data. Other wise num_inducing is ignored
+    .. Note:: Multiple independent outputs are allowed using columns of Y
+    """
+    def __init__(self, X, X_variance, Y, kernel=None, Z=None, num_inducing=10, Y_metadata=None, normalizer=None):
+        from ..core.parameterization.variational import NormalPosterior
+        if kernel is None:
+            kernel = kern.RBF(X.shape[1])
+
+        likelihood = likelihoods.Bernoulli()
+
+        if Z is None:
+            i = np.random.permutation(X.shape[0])[:num_inducing]
+            Z = X[i].copy()
+        else:
+            assert Z.shape[1] == X.shape[1]
+
+        X = NormalPosterior(X, X_variance)
+
+        SparseGP.__init__(self, X, Y, Z, kernel, likelihood,
+                          inference_method=expectation_propagation_dtc.EPDTC(),
+                          name='SparseGPClassification', Y_metadata=Y_metadata, normalizer=normalizer)
+
+    def parameters_changed(self):
+        #Compute the psi statistics for N once, but don't sum out N in psi2
+        self.psi0 = self.kern.psi0(self.Z, self.X)
+        self.psi1 = self.kern.psi1(self.Z, self.X)
+        self.psi2 = self.kern.psi2n(self.Z, self.X)
+        self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.Z, self.likelihood, self.Y, self.Y_metadata, psi0=self.psi0, psi1=self.psi1, psi2=self.psi2)
+        self._update_gradients()
+
+
+
+
+
diff --git a/GPy/models/sparse_gp_minibatch.py b/GPy/models/sparse_gp_minibatch.py
index adb92b30..be068a0e 100644
--- a/GPy/models/sparse_gp_minibatch.py
+++ b/GPy/models/sparse_gp_minibatch.py
@@ -99,13 +99,8 @@ class SparseGPMiniBatch(SparseGP):
         like them into this dictionary for inner use of the indices inside the
         algorithm.
         """
-        if psi2 is None:
-            psi2_sum_n = None
-        else:
-            psi2_sum_n = psi2.sum(axis=0)
-        posterior, log_marginal_likelihood, grad_dict = self.inference_method.inference(kern, X, Z, likelihood, Y, Y_metadata, Lm=Lm,
-                                                                                        dL_dKmm=dL_dKmm, psi0=psi0, psi1=psi1, psi2=psi2_sum_n, **kwargs)
-        return posterior, log_marginal_likelihood, grad_dict
+        return self.inference_method.inference(kern, X, Z, likelihood, Y, Y_metadata, Lm=Lm,
+                                               dL_dKmm=dL_dKmm, psi0=psi0, psi1=psi1, psi2=psi2, **kwargs)
 
     def _inner_take_over_or_update(self, full_values=None, current_values=None, value_indices=None):
         """
diff --git a/GPy/models/sparse_gp_regression.py b/GPy/models/sparse_gp_regression.py
index 49c3914c..faca7e9e 100644
--- a/GPy/models/sparse_gp_regression.py
+++ b/GPy/models/sparse_gp_regression.py
@@ -9,7 +9,6 @@ from .. import likelihoods
 from .. import kern
 from ..inference.latent_function_inference import VarDTC
 from ..core.parameterization.variational import NormalPosterior
-from GPy.inference.latent_function_inference.var_dtc_parallel import VarDTC_minibatch
 
 class SparseGPRegression(SparseGP_MPI):
     """
@@ -18,6 +17,7 @@ class SparseGPRegression(SparseGP_MPI):
     This is a thin wrapper around the SparseGP class, with a set of sensible defalts
 
     :param X: input observations
+    :param X_variance: input uncertainties, one per input X
     :param Y: observed values
     :param kernel: a GPy kernel, defaults to rbf+white
     :param Z: inducing inputs (optional, see note)
@@ -49,7 +49,7 @@ class SparseGPRegression(SparseGP_MPI):
 
         if not (X_variance is None):
             X = NormalPosterior(X,X_variance)
-            
+
         if mpi_comm is not None:
             from ..inference.latent_function_inference.var_dtc_parallel import VarDTC_minibatch
             infr = VarDTC_minibatch(mpi_comm=mpi_comm)
@@ -63,47 +63,4 @@ class SparseGPRegression(SparseGP_MPI):
         if isinstance(self.inference_method,VarDTC_minibatch):
             update_gradients_sparsegp(self, mpi_comm=self.mpi_comm)
         else:
-            super(SparseGPRegression, self).parameters_changed()
-
-class SparseGPRegressionUncertainInput(SparseGP):
-    """
-    Gaussian Process model for regression with Gaussian variance on the inputs (X_variance)
-
-    This is a thin wrapper around the SparseGP class, with a set of sensible defalts
-
-    """
-
-    def __init__(self, X, X_variance, Y, kernel=None, Z=None, num_inducing=10, normalizer=None):
-        """
-        :param X: input observations
-        :type X: np.ndarray (num_data x input_dim)
-        :param X_variance: The uncertainty in the measurements of X (Gaussian variance, optional)
-        :type X_variance: np.ndarray (num_data x input_dim)
-        :param Y: observed values
-        :param kernel: a GPy kernel, defaults to rbf+white
-        :param Z: inducing inputs (optional, see note)
-        :type Z: np.ndarray (num_inducing x input_dim) | None
-        :param num_inducing: number of inducing points (ignored if Z is passed, see note)
-        :type num_inducing: int
-        :rtype: model object
-
-        .. Note:: If no Z array is passed, num_inducing (default 10) points are selected from the data. Other wise num_inducing is ignored
-        .. Note:: Multiple independent outputs are allowed using columns of Y
-        """
-        num_data, input_dim = X.shape
-
-        # kern defaults to rbf (plus white for stability)
-        if kernel is None:
-            kernel = kern.RBF(input_dim) + kern.White(input_dim, variance=1e-3)
-
-        # Z defaults to a subset of the data
-        if Z is None:
-            i = np.random.permutation(num_data)[:min(num_inducing, num_data)]
-            Z = X[i].copy()
-        else:
-            assert Z.shape[1] == input_dim
-
-        likelihood = likelihoods.Gaussian()
-
-        SparseGP.__init__(self, X, Y, Z, kernel, likelihood, X_variance=X_variance, inference_method=VarDTC(), normalizer=normalizer)
-        self.ensure_default_constraints()
+            super(SparseGPRegression, self).parameters_changed()
\ No newline at end of file
diff --git a/GPy/plotting/matplot_dep/models_plots.py b/GPy/plotting/matplot_dep/models_plots.py
index a15146cf..c0864604 100644
--- a/GPy/plotting/matplot_dep/models_plots.py
+++ b/GPy/plotting/matplot_dep/models_plots.py
@@ -42,8 +42,12 @@ def plot_data(model, which_data_rows='all',
         fig = plt.figure(num=fignum)
         ax = fig.add_subplot(111)
 
-    #data
-    X = model.X
+    if hasattr(model, 'has_uncertain_inputs') and model.has_uncertain_inputs():
+        X = model.X.mean
+        X_variance = model.X.variance
+    else:
+        X = model.X
+        X_variance = None
     Y = model.Y
 
     #work out what the inputs are for plotting (1D or 2D)
@@ -54,9 +58,14 @@ def plot_data(model, which_data_rows='all',
     plots = {}
     #one dimensional plotting
     if len(free_dims) == 1:
-
+        plots['dataplot'] = []
+        if X_variance is not None: plots['xerrorbar'] = []
         for d in which_data_ycols:
-            plots['dataplot'] = ax.plot(X[which_data_rows,free_dims], Y[which_data_rows, d], data_symbol, mew=mew)
+            plots['dataplot'].append(ax.plot(X[which_data_rows, free_dims], Y[which_data_rows, d], data_symbol, mew=mew))
+            if X_variance is not None:
+                plots['xerrorbar'] = ax.errorbar(X[which_data_rows, free_dims].flatten(), Y[which_data_rows, which_data_ycols].flatten(),
+                            xerr=2 * np.sqrt(X_variance[which_data_rows, free_dims].flatten()),
+                            ecolor='k', fmt='none', elinewidth=.5, alpha=.5)
 
     #2D plotting
     elif len(free_dims) == 2:
@@ -219,10 +228,6 @@ def plot_fit(model, plot_limits=None, which_data_rows='all',
                 plots['xerrorbar'] = ax.errorbar(X[which_data_rows, free_dims].flatten(), m_X[which_data_rows, which_data_ycols].flatten(),
                             xerr=2 * np.sqrt(X_variance[which_data_rows, free_dims].flatten()),
                             ecolor='k', fmt=None, elinewidth=.5, alpha=.5)
-            else:
-                plots['xerrorbar'] = ax.errorbar(X[which_data_rows, free_dims].flatten(), Y[which_data_rows, which_data_ycols].flatten(),
-                            xerr=2 * np.sqrt(X_variance[which_data_rows, free_dims].flatten()),
-                            ecolor='k', fmt=None, elinewidth=.5, alpha=.5)
 
         #set the limits of the plot to some sensible values
         ymin, ymax = min(np.append(Y[which_data_rows, which_data_ycols].flatten(), lower)), max(np.append(Y[which_data_rows, which_data_ycols].flatten(), upper))
diff --git a/GPy/testing/model_tests.py b/GPy/testing/model_tests.py
index 60ec3214..d7339dd0 100644
--- a/GPy/testing/model_tests.py
+++ b/GPy/testing/model_tests.py
@@ -447,16 +447,14 @@ class GradientTests(np.testing.TestCase):
         rbflin = GPy.kern.RBF(2) + GPy.kern.Linear(2)
         self.check_model(rbflin, model_type='SparseGPRegression', dimension=2)
 
-    def test_SparseGPRegression_rbf_linear_white_kern_2D_uncertain_inputs(self):
+    def test_SparseGPRegression_rbf_white_kern_2D_uncertain_inputs(self):
         ''' Testing the sparse GP regression with rbf, linear kernel on 2d data with uncertain inputs'''
-        rbflin = GPy.kern.RBF(2) + GPy.kern.Linear(2)
-        raise unittest.SkipTest("This is not implemented yet!")
+        rbflin = GPy.kern.RBF(2) + GPy.kern.White(2)
         self.check_model(rbflin, model_type='SparseGPRegression', dimension=2, uncertain_inputs=1)
 
-    def test_SparseGPRegression_rbf_linear_white_kern_1D_uncertain_inputs(self):
+    def test_SparseGPRegression_rbf_white_kern_1D_uncertain_inputs(self):
         ''' Testing the sparse GP regression with rbf, linear kernel on 1d data with uncertain inputs'''
-        rbflin = GPy.kern.RBF(1) + GPy.kern.Linear(1)
-        raise unittest.SkipTest("This is not implemented yet!")
+        rbflin = GPy.kern.RBF(1) + GPy.kern.White(1)
         self.check_model(rbflin, model_type='SparseGPRegression', dimension=1, uncertain_inputs=1)
 
     def test_GPLVM_rbf_bias_white_kern_2D(self):
@@ -506,6 +504,17 @@ class GradientTests(np.testing.TestCase):
         m = GPy.models.SparseGPClassification(X, Y, kernel=kernel, Z=Z)
         self.assertTrue(m.checkgrad())
 
+    def test_sparse_EP_DTC_probit_uncertain_inputs(self):
+        N = 20
+        X = np.hstack([np.random.normal(5, 2, N / 2), np.random.normal(10, 2, N / 2)])[:, None]
+        Y = np.hstack([np.ones(N / 2), np.zeros(N / 2)])[:, None]
+        Z = np.linspace(0, 15, 4)[:, None]
+        X_var = np.random.uniform(0.1, 0.2, X.shape)
+        kernel = GPy.kern.RBF(1)
+        m = GPy.models.SparseGPClassificationUncertainInput(X, X_var, Y, kernel=kernel, Z=Z)
+        self.assertTrue(m.checkgrad())
+
+
     def test_multioutput_regression_1D(self):
         X1 = np.random.rand(50, 1) * 8
         X2 = np.random.rand(30, 1) * 5
diff --git a/setup.py b/setup.py
index 0432cbad..85fb3e19 100644
--- a/setup.py
+++ b/setup.py
@@ -37,8 +37,9 @@ else:
     link_args = ['-lgomp']
 
 ext_mods = [Extension(name='GPy.kern._src.stationary_cython',
-                      sources=['GPy/kern/_src/stationary_cython.c','GPy/kern/_src/stationary_utils.c'],
-                      include_dirs=[np.get_include()],
+                      sources=['GPy/kern/_src/stationary_cython.c',
+                               'GPy/kern/_src/stationary_utils.c'],
+                      include_dirs=[np.get_include(),'.'],
                       extra_compile_args=compile_flags,
                       extra_link_args = link_args),
             Extension(name='GPy.util.choleskies_cython',

From 79bfbfc7767d2c6594308a16784f54e953533da7 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Fri, 11 Sep 2015 15:26:04 +0100
Subject: [PATCH 02/22] [setup] include headers in source dist

---
 setup.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/setup.py b/setup.py
index 85fb3e19..7edd7066 100644
--- a/setup.py
+++ b/setup.py
@@ -44,16 +44,16 @@ ext_mods = [Extension(name='GPy.kern._src.stationary_cython',
                       extra_link_args = link_args),
             Extension(name='GPy.util.choleskies_cython',
                       sources=['GPy/util/choleskies_cython.c'],
-                      include_dirs=[np.get_include()],
+                      include_dirs=[np.get_include(),'.'],
                       extra_link_args = link_args,
                       extra_compile_args=compile_flags),
             Extension(name='GPy.util.linalg_cython',
                       sources=['GPy/util/linalg_cython.c'],
-                      include_dirs=[np.get_include()],
+                      include_dirs=[np.get_include(),'.'],
                       extra_compile_args=compile_flags),
             Extension(name='GPy.kern._src.coregionalize_cython',
                       sources=['GPy/kern/_src/coregionalize_cython.c'],
-                      include_dirs=[np.get_include()],
+                      include_dirs=[np.get_include(),'.'],
                       extra_compile_args=compile_flags)]
 
 setup(name = 'GPy',

From 8132084de669cdde6a953ab6d54f48a015b4b3ed Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Fri, 11 Sep 2015 15:47:07 +0100
Subject: [PATCH 03/22] [ep] now calling exact inference instead of copying
 code

---
 GPy/core/gp.py                                |  2 +-
 .../latent_function_inference/dtc.py          | 38 +++++++++----------
 .../exact_gaussian_inference.py               | 26 ++++---------
 .../expectation_propagation.py                | 23 ++++-------
 .../expectation_propagation_dtc.py            |  2 +-
 .../latent_function_inference/var_dtc.py      | 38 +++++++++----------
 GPy/likelihoods/bernoulli.py                  |  2 +-
 7 files changed, 56 insertions(+), 75 deletions(-)

diff --git a/GPy/core/gp.py b/GPy/core/gp.py
index d265161c..8a2e86c5 100644
--- a/GPy/core/gp.py
+++ b/GPy/core/gp.py
@@ -98,7 +98,7 @@ class GP(Model):
                 inference_method = exact_gaussian_inference.ExactGaussianInference()
             else:
                 inference_method = expectation_propagation.EP()
-                print("defaulting to ", inference_method, "for latent function inference")
+                print("defaulting to " + str(inference_method) + " for latent function inference")
         self.inference_method = inference_method
 
         logger.info("adding kernel and likelihood as parameters")
diff --git a/GPy/inference/latent_function_inference/dtc.py b/GPy/inference/latent_function_inference/dtc.py
index 0aa990c1..5f3e9ff7 100644
--- a/GPy/inference/latent_function_inference/dtc.py
+++ b/GPy/inference/latent_function_inference/dtc.py
@@ -28,8 +28,8 @@ class DTC(LatentFunctionInference):
         num_data, output_dim = Y.shape
 
         #make sure the noise is not hetero
-        beta = 1./likelihood.gaussian_variance(Y_metadata)
-        if beta.size > 1:
+        gaussian_variance = 1./likelihood.gaussian_variance(Y_metadata)
+        if gaussian_variance.size > 1:
             raise NotImplementedError("no hetero noise with this implementation of DTC")
 
         Kmm = kern.K(Z)
@@ -42,7 +42,7 @@ class DTC(LatentFunctionInference):
         Kmmi, L, Li, _ = pdinv(Kmm)
 
         # Compute A
-        LiUTbeta = np.dot(Li, U.T)*np.sqrt(beta)
+        LiUTbeta = np.dot(Li, U.T)*np.sqrt(gaussian_variance)
         A = tdot(LiUTbeta) + np.eye(num_inducing)
 
         # factor A
@@ -50,7 +50,7 @@ class DTC(LatentFunctionInference):
 
         # back substutue to get b, P, v
         tmp, _ = dtrtrs(L, Uy, lower=1)
-        b, _ = dtrtrs(LA, tmp*beta, lower=1)
+        b, _ = dtrtrs(LA, tmp*gaussian_variance, lower=1)
         tmp, _ = dtrtrs(LA, b, lower=1, trans=1)
         v, _ = dtrtrs(L, tmp, lower=1, trans=1)
         tmp, _ = dtrtrs(LA, Li, lower=1, trans=0)
@@ -59,8 +59,8 @@ class DTC(LatentFunctionInference):
         #compute log marginal
         log_marginal = -0.5*num_data*output_dim*np.log(2*np.pi) + \
                        -np.sum(np.log(np.diag(LA)))*output_dim + \
-                       0.5*num_data*output_dim*np.log(beta) + \
-                       -0.5*beta*np.sum(np.square(Y)) + \
+                       0.5*num_data*output_dim*np.log(gaussian_variance) + \
+                       -0.5*gaussian_variance*np.sum(np.square(Y)) + \
                        0.5*np.sum(np.square(b))
 
         # Compute dL_dKmm
@@ -70,11 +70,11 @@ class DTC(LatentFunctionInference):
         # Compute dL_dU
         vY = np.dot(v.reshape(-1,1),Y.T)
         dL_dU = vY - np.dot(vvT_P, U.T)
-        dL_dU *= beta
+        dL_dU *= gaussian_variance
 
         #compute dL_dR
         Uv = np.dot(U, v)
-        dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./beta + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1))*beta**2
+        dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./gaussian_variance + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1))*gaussian_variance**2
 
         dL_dthetaL = likelihood.exact_inference_gradients(dL_dR)
 
@@ -97,8 +97,8 @@ class vDTC(object):
         num_data, output_dim = Y.shape
 
         #make sure the noise is not hetero
-        beta = 1./likelihood.gaussian_variance(Y_metadata)
-        if beta.size > 1:
+        gaussian_variance = 1./likelihood.gaussian_variance(Y_metadata)
+        if gaussian_variance.size > 1:
             raise NotImplementedError("no hetero noise with this implementation of DTC")
 
         Kmm = kern.K(Z)
@@ -111,9 +111,9 @@ class vDTC(object):
         Kmmi, L, Li, _ = pdinv(Kmm)
 
         # Compute A
-        LiUTbeta = np.dot(Li, U.T)*np.sqrt(beta)
+        LiUTbeta = np.dot(Li, U.T)*np.sqrt(gaussian_variance)
         A_ = tdot(LiUTbeta)
-        trace_term = -0.5*(np.sum(Knn)*beta - np.trace(A_))
+        trace_term = -0.5*(np.sum(Knn)*gaussian_variance - np.trace(A_))
         A = A_ + np.eye(num_inducing)
 
         # factor A
@@ -121,7 +121,7 @@ class vDTC(object):
 
         # back substutue to get b, P, v
         tmp, _ = dtrtrs(L, Uy, lower=1)
-        b, _ = dtrtrs(LA, tmp*beta, lower=1)
+        b, _ = dtrtrs(LA, tmp*gaussian_variance, lower=1)
         tmp, _ = dtrtrs(LA, b, lower=1, trans=1)
         v, _ = dtrtrs(L, tmp, lower=1, trans=1)
         tmp, _ = dtrtrs(LA, Li, lower=1, trans=0)
@@ -131,8 +131,8 @@ class vDTC(object):
         #compute log marginal
         log_marginal = -0.5*num_data*output_dim*np.log(2*np.pi) + \
                        -np.sum(np.log(np.diag(LA)))*output_dim + \
-                       0.5*num_data*output_dim*np.log(beta) + \
-                       -0.5*beta*np.sum(np.square(Y)) + \
+                       0.5*num_data*output_dim*np.log(gaussian_variance) + \
+                       -0.5*gaussian_variance*np.sum(np.square(Y)) + \
                        0.5*np.sum(np.square(b)) + \
                        trace_term
 
@@ -145,15 +145,15 @@ class vDTC(object):
         vY = np.dot(v.reshape(-1,1),Y.T)
         #dL_dU = vY - np.dot(vvT_P, U.T)
         dL_dU = vY - np.dot(vvT_P - Kmmi, U.T)
-        dL_dU *= beta
+        dL_dU *= gaussian_variance
 
         #compute dL_dR
         Uv = np.dot(U, v)
-        dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./beta + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1) )*beta**2
-        dL_dR -=beta*trace_term/num_data
+        dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./gaussian_variance + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1) )*gaussian_variance**2
+        dL_dR -=gaussian_variance*trace_term/num_data
 
         dL_dthetaL = likelihood.exact_inference_gradients(dL_dR)
-        grad_dict = {'dL_dKmm': dL_dK, 'dL_dKdiag':np.zeros_like(Knn) + -0.5*beta, 'dL_dKnm':dL_dU.T, 'dL_dthetaL':dL_dthetaL}
+        grad_dict = {'dL_dKmm': dL_dK, 'dL_dKdiag':np.zeros_like(Knn) + -0.5*gaussian_variance, 'dL_dKnm':dL_dU.T, 'dL_dthetaL':dL_dthetaL}
 
         #construct a posterior object
         post = Posterior(woodbury_inv=Kmmi-P, woodbury_vector=v, K=Kmm, mean=None, cov=None, K_chol=L)
diff --git a/GPy/inference/latent_function_inference/exact_gaussian_inference.py b/GPy/inference/latent_function_inference/exact_gaussian_inference.py
index 343387a7..375e1e70 100644
--- a/GPy/inference/latent_function_inference/exact_gaussian_inference.py
+++ b/GPy/inference/latent_function_inference/exact_gaussian_inference.py
@@ -22,21 +22,7 @@ class ExactGaussianInference(LatentFunctionInference):
     def __init__(self):
         pass#self._YYTfactor_cache = caching.cache()
 
-    def get_YYTfactor(self, Y):
-        """
-        find a matrix L which satisfies LL^T = YY^T.
-
-        Note that L may have fewer columns than Y, else L=Y.
-        """
-        N, D = Y.shape
-        if (N>D):
-            return Y
-        else:
-            #if Y in self.cache, return self.Cache[Y], else store Y in cache and return L.
-            #print "WARNING: N>D of Y, we need caching of L, such that L*L^T = Y, returning Y still!"
-            return Y
-
-    def inference(self, kern, X, likelihood, Y, mean_function=None, Y_metadata=None):
+    def inference(self, kern, X, likelihood, Y, mean_function=None, Y_metadata=None, K=None, gaussian_variance=None):
         """
         Returns a Posterior class containing essential quantities of the posterior
         """
@@ -46,13 +32,17 @@ class ExactGaussianInference(LatentFunctionInference):
         else:
             m = mean_function.f(X)
 
+        if gaussian_variance is None:
+            gaussian_variance = likelihood.gaussian_variance(Y_metadata)
 
-        YYT_factor = self.get_YYTfactor(Y-m)
+        YYT_factor = Y-m
 
-        K = kern.K(X)
+        if K is None:
+            K = kern.K(X)
 
         Ky = K.copy()
-        diag.add(Ky, likelihood.gaussian_variance(Y_metadata)+1e-8)
+        diag.add(Ky, gaussian_variance+1e-8)
+
         Wi, LW, LWi, W_logdet = pdinv(Ky)
 
         alpha, _ = dpotrs(LW, YYT_factor, lower=1)
diff --git a/GPy/inference/latent_function_inference/expectation_propagation.py b/GPy/inference/latent_function_inference/expectation_propagation.py
index f621dcc7..089f325e 100644
--- a/GPy/inference/latent_function_inference/expectation_propagation.py
+++ b/GPy/inference/latent_function_inference/expectation_propagation.py
@@ -3,11 +3,11 @@
 import numpy as np
 from ...util.linalg import pdinv,jitchol,DSYR,tdot,dtrtrs, dpotrs
 from .posterior import Posterior
-from . import LatentFunctionInference
+from . import ExactGaussianInference
 from ...util import diag
 log_2_pi = np.log(2*np.pi)
 
-class EP(LatentFunctionInference):
+class EP(ExactGaussianInference):
     def __init__(self, epsilon=1e-6, eta=1., delta=1.):
         """
         The expectation-propagation algorithm.
@@ -20,6 +20,7 @@ class EP(LatentFunctionInference):
         :param delta: damping EP updates factor.
         :type delta: float64
         """
+        super(EP, self).__init__()
         self.epsilon, self.eta, self.delta = epsilon, eta, delta
         self.reset()
 
@@ -34,12 +35,12 @@ class EP(LatentFunctionInference):
         # TODO: update approximation in the end as well? Maybe even with a switch?
         pass
 
-    def inference(self, kern, X, likelihood, Y, mean_function=None, Y_metadata=None, Z=None):
-        assert mean_function is None, "inference with a mean function not implemented"
+    def inference(self, kern, X, likelihood, Y, mean_function=None, Y_metadata=None, gaussian_variance=None, K=None):
         num_data, output_dim = Y.shape
         assert output_dim ==1, "ep in 1D only (for now!)"
 
-        K = kern.K(X)
+        if K is None:
+            K = kern.K(X)
 
         if self._ep_approximation is None:
             #if we don't yet have the results of runnign EP, run EP and store the computed factors in self._ep_approximation
@@ -48,17 +49,7 @@ class EP(LatentFunctionInference):
             #if we've already run EP, just use the existing approximation stored in self._ep_approximation
             mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation
 
-        Wi, LW, LWi, W_logdet = pdinv(K + np.diag(1./tau_tilde))
-
-        alpha, _ = dpotrs(LW, mu_tilde, lower=1)
-
-        log_marginal =  0.5*(-num_data * log_2_pi - W_logdet - np.sum(alpha * mu_tilde)) # TODO: add log Z_hat??
-
-        dL_dK = 0.5 * (tdot(alpha[:,None]) - Wi)
-
-        dL_dthetaL = np.zeros(likelihood.size)#TODO: derivatives of the likelihood parameters
-
-        return Posterior(woodbury_inv=Wi, woodbury_vector=alpha, K=K), log_marginal, {'dL_dK':dL_dK, 'dL_dthetaL':dL_dthetaL}
+        return super(EP, self).inference(kern, X, likelihood, mu_tilde[:,None], mean_function=mean_function, Y_metadata=Y_metadata, gaussian_variance=1./tau_tilde, K=K)
 
     def expectation_propagation(self, K, Y, likelihood, Y_metadata):
 
diff --git a/GPy/inference/latent_function_inference/expectation_propagation_dtc.py b/GPy/inference/latent_function_inference/expectation_propagation_dtc.py
index af71f395..7b64d8c5 100644
--- a/GPy/inference/latent_function_inference/expectation_propagation_dtc.py
+++ b/GPy/inference/latent_function_inference/expectation_propagation_dtc.py
@@ -46,7 +46,7 @@ class EPDTC(VarDTC):
         return super(EPDTC, self).inference(kern, X, Z, likelihood, mu_tilde,
                                             mean_function=mean_function,
                                             Y_metadata=Y_metadata,
-                                            beta=tau_tilde,
+                                            gaussian_variance=tau_tilde,
                                             Lm=Lm, dL_dKmm=dL_dKmm,
                                             psi0=psi0, psi1=psi1, psi2=psi2)
 
diff --git a/GPy/inference/latent_function_inference/var_dtc.py b/GPy/inference/latent_function_inference/var_dtc.py
index f46d91f1..c50f0e7d 100644
--- a/GPy/inference/latent_function_inference/var_dtc.py
+++ b/GPy/inference/latent_function_inference/var_dtc.py
@@ -64,7 +64,7 @@ class VarDTC(LatentFunctionInference):
     def get_VVTfactor(self, Y, prec):
         return Y * prec # TODO chache this, and make it effective
 
-    def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None, mean_function=None, beta=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
+    def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None, mean_function=None, gaussian_variance=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
         assert mean_function is None, "inference with a mean function not implemented"
 
         num_data, output_dim = Y.shape
@@ -72,16 +72,16 @@ class VarDTC(LatentFunctionInference):
 
         uncertain_inputs = isinstance(X, VariationalPosterior)
 
-        if beta is None:
+        if gaussian_variance is None:
             #assume Gaussian likelihood
-            beta = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), self.const_jitter)
+            gaussian_variance = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), self.const_jitter)
 
-        if beta.ndim == 1:
-            beta = beta[:, None]
-        het_noise = beta.size > 1
+        if gaussian_variance.ndim == 1:
+            gaussian_variance = gaussian_variance[:, None]
+        het_noise = gaussian_variance.size > 1
 
-        VVT_factor = beta*Y
-        #VVT_factor = beta*Y
+        VVT_factor = gaussian_variance*Y
+        #VVT_factor = gaussian_variance*Y
         trYYT = self.get_trYYT(Y)
 
         # kernel computations, using BGPLVM notation
@@ -98,16 +98,16 @@ class VarDTC(LatentFunctionInference):
                 psi1 = kern.psi1(Z, X)
             if het_noise:
                 if psi2 is None:
-                    psi2_beta = (kern.psi2n(Z, X) * beta[:, :, None]).sum(0)
+                    psi2_beta = (kern.psi2n(Z, X) * gaussian_variance[:, :, None]).sum(0)
                 else:
-                    psi2_beta = (psi2 * beta[:, :, None]).sum(0)
+                    psi2_beta = (psi2 * gaussian_variance[:, :, None]).sum(0)
             else:
                 if psi2 is None:
-                    psi2_beta = kern.psi2(Z,X) * beta
+                    psi2_beta = kern.psi2(Z,X) * gaussian_variance
                 elif psi2.ndim == 3:
-                    psi2_beta = psi2.sum(0) * beta
+                    psi2_beta = psi2.sum(0) * gaussian_variance
                 else:
-                    psi2_beta = psi2 * beta
+                    psi2_beta = psi2 * gaussian_variance
             LmInv = dtrtri(Lm)
             A = LmInv.dot(psi2_beta.dot(LmInv.T))
         else:
@@ -116,9 +116,9 @@ class VarDTC(LatentFunctionInference):
             if psi1 is None:
                 psi1 = kern.K(X, Z)
             if het_noise:
-                tmp = psi1 * (np.sqrt(beta))
+                tmp = psi1 * (np.sqrt(gaussian_variance))
             else:
-                tmp = psi1 * (np.sqrt(beta))
+                tmp = psi1 * (np.sqrt(gaussian_variance))
             tmp, _ = dtrtrs(Lm, tmp.T, lower=1)
             A = tdot(tmp) #print A.sum()
 
@@ -144,19 +144,19 @@ class VarDTC(LatentFunctionInference):
             dL_dKmm = backsub_both_sides(Lm, delit)
 
         # derivatives of L w.r.t. psi
-        dL_dpsi0, dL_dpsi1, dL_dpsi2 = _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm,
+        dL_dpsi0, dL_dpsi1, dL_dpsi2 = _compute_dL_dpsi(num_inducing, num_data, output_dim, gaussian_variance, Lm,
             VVT_factor, Cpsi1Vf, DBi_plus_BiPBi,
             psi1, het_noise, uncertain_inputs)
 
         # log marginal likelihood
-        log_marginal = _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise,
+        log_marginal = _compute_log_marginal_likelihood(likelihood, num_data, output_dim, gaussian_variance, het_noise,
             psi0, A, LB, trYYT, data_fit, Y)
 
         #noise derivatives
         dL_dR = _compute_dL_dR(likelihood,
             het_noise, uncertain_inputs, LB,
             _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A,
-            psi0, psi1, beta,
+            psi0, psi1, gaussian_variance,
             data_fit, num_data, output_dim, trYYT, Y, VVT_factor)
 
         dL_dthetaL = likelihood.exact_inference_gradients(dL_dR,Y_metadata)
@@ -181,7 +181,7 @@ class VarDTC(LatentFunctionInference):
         else:
             print('foobar')
             import ipdb; ipdb.set_trace()
-            psi1V = np.dot(Y.T*beta, psi1).T
+            psi1V = np.dot(Y.T*gaussian_variance, psi1).T
             tmp, _ = dtrtrs(Lm, psi1V, lower=1, trans=0)
             tmp, _ = dpotrs(LB, tmp, lower=1)
             woodbury_vector, _ = dtrtrs(Lm, tmp, lower=1, trans=1)
diff --git a/GPy/likelihoods/bernoulli.py b/GPy/likelihoods/bernoulli.py
index 1c55a89a..856de40f 100644
--- a/GPy/likelihoods/bernoulli.py
+++ b/GPy/likelihoods/bernoulli.py
@@ -258,4 +258,4 @@ class Bernoulli(Likelihood):
         return Ysim.reshape(orig_shape)
 
     def exact_inference_gradients(self, dL_dKdiag,Y_metadata=None):
-        pass
+        return np.zeros(self.size)

From 69f6cfa6f7671b32a77ff6bfdab4a114675abab5 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Fri, 11 Sep 2015 16:59:55 +0100
Subject: [PATCH 04/22] [inference] changed gaussian variance to precision
 (which it really is)

---
 .../latent_function_inference/dtc.py          | 38 +++++++++----------
 .../exact_gaussian_inference.py               |  8 ++--
 .../expectation_propagation.py                |  4 +-
 .../expectation_propagation_dtc.py            |  2 +-
 .../latent_function_inference/var_dtc.py      | 38 +++++++++----------
 5 files changed, 45 insertions(+), 45 deletions(-)

diff --git a/GPy/inference/latent_function_inference/dtc.py b/GPy/inference/latent_function_inference/dtc.py
index 5f3e9ff7..6149ce88 100644
--- a/GPy/inference/latent_function_inference/dtc.py
+++ b/GPy/inference/latent_function_inference/dtc.py
@@ -28,8 +28,8 @@ class DTC(LatentFunctionInference):
         num_data, output_dim = Y.shape
 
         #make sure the noise is not hetero
-        gaussian_variance = 1./likelihood.gaussian_variance(Y_metadata)
-        if gaussian_variance.size > 1:
+        precision = 1./likelihood.gaussian_variance(Y_metadata)
+        if precision.size > 1:
             raise NotImplementedError("no hetero noise with this implementation of DTC")
 
         Kmm = kern.K(Z)
@@ -42,7 +42,7 @@ class DTC(LatentFunctionInference):
         Kmmi, L, Li, _ = pdinv(Kmm)
 
         # Compute A
-        LiUTbeta = np.dot(Li, U.T)*np.sqrt(gaussian_variance)
+        LiUTbeta = np.dot(Li, U.T)*np.sqrt(precision)
         A = tdot(LiUTbeta) + np.eye(num_inducing)
 
         # factor A
@@ -50,7 +50,7 @@ class DTC(LatentFunctionInference):
 
         # back substutue to get b, P, v
         tmp, _ = dtrtrs(L, Uy, lower=1)
-        b, _ = dtrtrs(LA, tmp*gaussian_variance, lower=1)
+        b, _ = dtrtrs(LA, tmp*precision, lower=1)
         tmp, _ = dtrtrs(LA, b, lower=1, trans=1)
         v, _ = dtrtrs(L, tmp, lower=1, trans=1)
         tmp, _ = dtrtrs(LA, Li, lower=1, trans=0)
@@ -59,8 +59,8 @@ class DTC(LatentFunctionInference):
         #compute log marginal
         log_marginal = -0.5*num_data*output_dim*np.log(2*np.pi) + \
                        -np.sum(np.log(np.diag(LA)))*output_dim + \
-                       0.5*num_data*output_dim*np.log(gaussian_variance) + \
-                       -0.5*gaussian_variance*np.sum(np.square(Y)) + \
+                       0.5*num_data*output_dim*np.log(precision) + \
+                       -0.5*precision*np.sum(np.square(Y)) + \
                        0.5*np.sum(np.square(b))
 
         # Compute dL_dKmm
@@ -70,11 +70,11 @@ class DTC(LatentFunctionInference):
         # Compute dL_dU
         vY = np.dot(v.reshape(-1,1),Y.T)
         dL_dU = vY - np.dot(vvT_P, U.T)
-        dL_dU *= gaussian_variance
+        dL_dU *= precision
 
         #compute dL_dR
         Uv = np.dot(U, v)
-        dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./gaussian_variance + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1))*gaussian_variance**2
+        dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./precision + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1))*precision**2
 
         dL_dthetaL = likelihood.exact_inference_gradients(dL_dR)
 
@@ -97,8 +97,8 @@ class vDTC(object):
         num_data, output_dim = Y.shape
 
         #make sure the noise is not hetero
-        gaussian_variance = 1./likelihood.gaussian_variance(Y_metadata)
-        if gaussian_variance.size > 1:
+        precision = 1./likelihood.gaussian_variance(Y_metadata)
+        if precision.size > 1:
             raise NotImplementedError("no hetero noise with this implementation of DTC")
 
         Kmm = kern.K(Z)
@@ -111,9 +111,9 @@ class vDTC(object):
         Kmmi, L, Li, _ = pdinv(Kmm)
 
         # Compute A
-        LiUTbeta = np.dot(Li, U.T)*np.sqrt(gaussian_variance)
+        LiUTbeta = np.dot(Li, U.T)*np.sqrt(precision)
         A_ = tdot(LiUTbeta)
-        trace_term = -0.5*(np.sum(Knn)*gaussian_variance - np.trace(A_))
+        trace_term = -0.5*(np.sum(Knn)*precision - np.trace(A_))
         A = A_ + np.eye(num_inducing)
 
         # factor A
@@ -121,7 +121,7 @@ class vDTC(object):
 
         # back substutue to get b, P, v
         tmp, _ = dtrtrs(L, Uy, lower=1)
-        b, _ = dtrtrs(LA, tmp*gaussian_variance, lower=1)
+        b, _ = dtrtrs(LA, tmp*precision, lower=1)
         tmp, _ = dtrtrs(LA, b, lower=1, trans=1)
         v, _ = dtrtrs(L, tmp, lower=1, trans=1)
         tmp, _ = dtrtrs(LA, Li, lower=1, trans=0)
@@ -131,8 +131,8 @@ class vDTC(object):
         #compute log marginal
         log_marginal = -0.5*num_data*output_dim*np.log(2*np.pi) + \
                        -np.sum(np.log(np.diag(LA)))*output_dim + \
-                       0.5*num_data*output_dim*np.log(gaussian_variance) + \
-                       -0.5*gaussian_variance*np.sum(np.square(Y)) + \
+                       0.5*num_data*output_dim*np.log(precision) + \
+                       -0.5*precision*np.sum(np.square(Y)) + \
                        0.5*np.sum(np.square(b)) + \
                        trace_term
 
@@ -145,15 +145,15 @@ class vDTC(object):
         vY = np.dot(v.reshape(-1,1),Y.T)
         #dL_dU = vY - np.dot(vvT_P, U.T)
         dL_dU = vY - np.dot(vvT_P - Kmmi, U.T)
-        dL_dU *= gaussian_variance
+        dL_dU *= precision
 
         #compute dL_dR
         Uv = np.dot(U, v)
-        dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./gaussian_variance + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1) )*gaussian_variance**2
-        dL_dR -=gaussian_variance*trace_term/num_data
+        dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./precision + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1) )*precision**2
+        dL_dR -=precision*trace_term/num_data
 
         dL_dthetaL = likelihood.exact_inference_gradients(dL_dR)
-        grad_dict = {'dL_dKmm': dL_dK, 'dL_dKdiag':np.zeros_like(Knn) + -0.5*gaussian_variance, 'dL_dKnm':dL_dU.T, 'dL_dthetaL':dL_dthetaL}
+        grad_dict = {'dL_dKmm': dL_dK, 'dL_dKdiag':np.zeros_like(Knn) + -0.5*precision, 'dL_dKnm':dL_dU.T, 'dL_dthetaL':dL_dthetaL}
 
         #construct a posterior object
         post = Posterior(woodbury_inv=Kmmi-P, woodbury_vector=v, K=Kmm, mean=None, cov=None, K_chol=L)
diff --git a/GPy/inference/latent_function_inference/exact_gaussian_inference.py b/GPy/inference/latent_function_inference/exact_gaussian_inference.py
index 375e1e70..2d8fb691 100644
--- a/GPy/inference/latent_function_inference/exact_gaussian_inference.py
+++ b/GPy/inference/latent_function_inference/exact_gaussian_inference.py
@@ -22,7 +22,7 @@ class ExactGaussianInference(LatentFunctionInference):
     def __init__(self):
         pass#self._YYTfactor_cache = caching.cache()
 
-    def inference(self, kern, X, likelihood, Y, mean_function=None, Y_metadata=None, K=None, gaussian_variance=None):
+    def inference(self, kern, X, likelihood, Y, mean_function=None, Y_metadata=None, K=None, precision=None):
         """
         Returns a Posterior class containing essential quantities of the posterior
         """
@@ -32,8 +32,8 @@ class ExactGaussianInference(LatentFunctionInference):
         else:
             m = mean_function.f(X)
 
-        if gaussian_variance is None:
-            gaussian_variance = likelihood.gaussian_variance(Y_metadata)
+        if precision is None:
+            precision = likelihood.gaussian_variance(Y_metadata)
 
         YYT_factor = Y-m
 
@@ -41,7 +41,7 @@ class ExactGaussianInference(LatentFunctionInference):
             K = kern.K(X)
 
         Ky = K.copy()
-        diag.add(Ky, gaussian_variance+1e-8)
+        diag.add(Ky, precision+1e-8)
 
         Wi, LW, LWi, W_logdet = pdinv(Ky)
 
diff --git a/GPy/inference/latent_function_inference/expectation_propagation.py b/GPy/inference/latent_function_inference/expectation_propagation.py
index 089f325e..bb289e12 100644
--- a/GPy/inference/latent_function_inference/expectation_propagation.py
+++ b/GPy/inference/latent_function_inference/expectation_propagation.py
@@ -35,7 +35,7 @@ class EP(ExactGaussianInference):
         # TODO: update approximation in the end as well? Maybe even with a switch?
         pass
 
-    def inference(self, kern, X, likelihood, Y, mean_function=None, Y_metadata=None, gaussian_variance=None, K=None):
+    def inference(self, kern, X, likelihood, Y, mean_function=None, Y_metadata=None, precision=None, K=None):
         num_data, output_dim = Y.shape
         assert output_dim ==1, "ep in 1D only (for now!)"
 
@@ -49,7 +49,7 @@ class EP(ExactGaussianInference):
             #if we've already run EP, just use the existing approximation stored in self._ep_approximation
             mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation
 
-        return super(EP, self).inference(kern, X, likelihood, mu_tilde[:,None], mean_function=mean_function, Y_metadata=Y_metadata, gaussian_variance=1./tau_tilde, K=K)
+        return super(EP, self).inference(kern, X, likelihood, mu_tilde[:,None], mean_function=mean_function, Y_metadata=Y_metadata, precision=1./tau_tilde, K=K)
 
     def expectation_propagation(self, K, Y, likelihood, Y_metadata):
 
diff --git a/GPy/inference/latent_function_inference/expectation_propagation_dtc.py b/GPy/inference/latent_function_inference/expectation_propagation_dtc.py
index 7b64d8c5..0f141824 100644
--- a/GPy/inference/latent_function_inference/expectation_propagation_dtc.py
+++ b/GPy/inference/latent_function_inference/expectation_propagation_dtc.py
@@ -46,7 +46,7 @@ class EPDTC(VarDTC):
         return super(EPDTC, self).inference(kern, X, Z, likelihood, mu_tilde,
                                             mean_function=mean_function,
                                             Y_metadata=Y_metadata,
-                                            gaussian_variance=tau_tilde,
+                                            precision=tau_tilde,
                                             Lm=Lm, dL_dKmm=dL_dKmm,
                                             psi0=psi0, psi1=psi1, psi2=psi2)
 
diff --git a/GPy/inference/latent_function_inference/var_dtc.py b/GPy/inference/latent_function_inference/var_dtc.py
index c50f0e7d..bb114050 100644
--- a/GPy/inference/latent_function_inference/var_dtc.py
+++ b/GPy/inference/latent_function_inference/var_dtc.py
@@ -64,7 +64,7 @@ class VarDTC(LatentFunctionInference):
     def get_VVTfactor(self, Y, prec):
         return Y * prec # TODO chache this, and make it effective
 
-    def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None, mean_function=None, gaussian_variance=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
+    def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None, mean_function=None, precision=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
         assert mean_function is None, "inference with a mean function not implemented"
 
         num_data, output_dim = Y.shape
@@ -72,16 +72,16 @@ class VarDTC(LatentFunctionInference):
 
         uncertain_inputs = isinstance(X, VariationalPosterior)
 
-        if gaussian_variance is None:
+        if precision is None:
             #assume Gaussian likelihood
-            gaussian_variance = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), self.const_jitter)
+            precision = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), self.const_jitter)
 
-        if gaussian_variance.ndim == 1:
-            gaussian_variance = gaussian_variance[:, None]
-        het_noise = gaussian_variance.size > 1
+        if precision.ndim == 1:
+            precision = precision[:, None]
+        het_noise = precision.size > 1
 
-        VVT_factor = gaussian_variance*Y
-        #VVT_factor = gaussian_variance*Y
+        VVT_factor = precision*Y
+        #VVT_factor = precision*Y
         trYYT = self.get_trYYT(Y)
 
         # kernel computations, using BGPLVM notation
@@ -98,16 +98,16 @@ class VarDTC(LatentFunctionInference):
                 psi1 = kern.psi1(Z, X)
             if het_noise:
                 if psi2 is None:
-                    psi2_beta = (kern.psi2n(Z, X) * gaussian_variance[:, :, None]).sum(0)
+                    psi2_beta = (kern.psi2n(Z, X) * precision[:, :, None]).sum(0)
                 else:
-                    psi2_beta = (psi2 * gaussian_variance[:, :, None]).sum(0)
+                    psi2_beta = (psi2 * precision[:, :, None]).sum(0)
             else:
                 if psi2 is None:
-                    psi2_beta = kern.psi2(Z,X) * gaussian_variance
+                    psi2_beta = kern.psi2(Z,X) * precision
                 elif psi2.ndim == 3:
-                    psi2_beta = psi2.sum(0) * gaussian_variance
+                    psi2_beta = psi2.sum(0) * precision
                 else:
-                    psi2_beta = psi2 * gaussian_variance
+                    psi2_beta = psi2 * precision
             LmInv = dtrtri(Lm)
             A = LmInv.dot(psi2_beta.dot(LmInv.T))
         else:
@@ -116,9 +116,9 @@ class VarDTC(LatentFunctionInference):
             if psi1 is None:
                 psi1 = kern.K(X, Z)
             if het_noise:
-                tmp = psi1 * (np.sqrt(gaussian_variance))
+                tmp = psi1 * (np.sqrt(precision))
             else:
-                tmp = psi1 * (np.sqrt(gaussian_variance))
+                tmp = psi1 * (np.sqrt(precision))
             tmp, _ = dtrtrs(Lm, tmp.T, lower=1)
             A = tdot(tmp) #print A.sum()
 
@@ -144,19 +144,19 @@ class VarDTC(LatentFunctionInference):
             dL_dKmm = backsub_both_sides(Lm, delit)
 
         # derivatives of L w.r.t. psi
-        dL_dpsi0, dL_dpsi1, dL_dpsi2 = _compute_dL_dpsi(num_inducing, num_data, output_dim, gaussian_variance, Lm,
+        dL_dpsi0, dL_dpsi1, dL_dpsi2 = _compute_dL_dpsi(num_inducing, num_data, output_dim, precision, Lm,
             VVT_factor, Cpsi1Vf, DBi_plus_BiPBi,
             psi1, het_noise, uncertain_inputs)
 
         # log marginal likelihood
-        log_marginal = _compute_log_marginal_likelihood(likelihood, num_data, output_dim, gaussian_variance, het_noise,
+        log_marginal = _compute_log_marginal_likelihood(likelihood, num_data, output_dim, precision, het_noise,
             psi0, A, LB, trYYT, data_fit, Y)
 
         #noise derivatives
         dL_dR = _compute_dL_dR(likelihood,
             het_noise, uncertain_inputs, LB,
             _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A,
-            psi0, psi1, gaussian_variance,
+            psi0, psi1, precision,
             data_fit, num_data, output_dim, trYYT, Y, VVT_factor)
 
         dL_dthetaL = likelihood.exact_inference_gradients(dL_dR,Y_metadata)
@@ -181,7 +181,7 @@ class VarDTC(LatentFunctionInference):
         else:
             print('foobar')
             import ipdb; ipdb.set_trace()
-            psi1V = np.dot(Y.T*gaussian_variance, psi1).T
+            psi1V = np.dot(Y.T*precision, psi1).T
             tmp, _ = dtrtrs(Lm, psi1V, lower=1, trans=0)
             tmp, _ = dpotrs(LB, tmp, lower=1)
             woodbury_vector, _ = dtrtrs(Lm, tmp, lower=1, trans=1)

From 383cf41dab7fb8dda9b53b900d89b244756772a1 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Fri, 11 Sep 2015 17:13:21 +0100
Subject: [PATCH 05/22] [#186] fixed distribution across files and added base
 class for reusability

---
 .../latent_function_inference/__init__.py     |   3 +-
 .../expectation_propagation.py                | 129 +++++++++++++++-
 .../expectation_propagation_dtc.py            | 142 ------------------
 GPy/models/sparse_gp_classification.py        |   7 +-
 4 files changed, 128 insertions(+), 153 deletions(-)
 delete mode 100644 GPy/inference/latent_function_inference/expectation_propagation_dtc.py

diff --git a/GPy/inference/latent_function_inference/__init__.py b/GPy/inference/latent_function_inference/__init__.py
index 7bdd6ff2..eabc6cc9 100644
--- a/GPy/inference/latent_function_inference/__init__.py
+++ b/GPy/inference/latent_function_inference/__init__.py
@@ -64,8 +64,7 @@ class InferenceMethodList(LatentFunctionInference, list):
 from .exact_gaussian_inference import ExactGaussianInference
 from .laplace import Laplace,LaplaceBlock
 from GPy.inference.latent_function_inference.var_dtc import VarDTC
-from .expectation_propagation import EP
-from .expectation_propagation_dtc import EPDTC
+from .expectation_propagation import EP, EPDTC
 from .dtc import DTC
 from .fitc import FITC
 from .var_dtc_parallel import VarDTC_minibatch
diff --git a/GPy/inference/latent_function_inference/expectation_propagation.py b/GPy/inference/latent_function_inference/expectation_propagation.py
index bb289e12..d293d4de 100644
--- a/GPy/inference/latent_function_inference/expectation_propagation.py
+++ b/GPy/inference/latent_function_inference/expectation_propagation.py
@@ -1,13 +1,14 @@
 # Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt).
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 import numpy as np
-from ...util.linalg import pdinv,jitchol,DSYR,tdot,dtrtrs, dpotrs
-from .posterior import Posterior
-from . import ExactGaussianInference
+from ...util.linalg import jitchol, DSYR, dtrtrs, dtrtri
+from ...core.parameterization.observable_array import ObsAr
+from . import ExactGaussianInference, VarDTC
 from ...util import diag
+
 log_2_pi = np.log(2*np.pi)
 
-class EP(ExactGaussianInference):
+class EPBase(object):
     def __init__(self, epsilon=1e-6, eta=1., delta=1.):
         """
         The expectation-propagation algorithm.
@@ -20,7 +21,7 @@ class EP(ExactGaussianInference):
         :param delta: damping EP updates factor.
         :type delta: float64
         """
-        super(EP, self).__init__()
+        super(EPBase, self).__init__()
         self.epsilon, self.eta, self.delta = epsilon, eta, delta
         self.reset()
 
@@ -35,6 +36,7 @@ class EP(ExactGaussianInference):
         # TODO: update approximation in the end as well? Maybe even with a switch?
         pass
 
+class EP(EPBase, ExactGaussianInference):
     def inference(self, kern, X, likelihood, Y, mean_function=None, Y_metadata=None, precision=None, K=None):
         num_data, output_dim = Y.shape
         assert output_dim ==1, "ep in 1D only (for now!)"
@@ -116,3 +118,120 @@ class EP(ExactGaussianInference):
 
         mu_tilde = v_tilde/tau_tilde
         return mu, Sigma, mu_tilde, tau_tilde, Z_hat
+
+class EPDTC(EPBase, VarDTC):
+    def inference(self, kern, X, Z, likelihood, Y, mean_function=None, Y_metadata=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
+        assert Y.shape[1]==1, "ep in 1D only (for now!)"
+
+        Kmm = kern.K(Z)
+        if psi1 is None:
+            try:
+                Kmn = kern.K(Z, X)
+            except TypeError:
+                Kmn = kern.psi1(Z, X).T
+        else:
+            Kmn = psi1.T
+
+        if self._ep_approximation is None:
+            mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation = self.expectation_propagation(Kmm, Kmn, Y, likelihood, Y_metadata)
+        else:
+            mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation
+
+        return super(EPDTC, self).inference(kern, X, Z, likelihood, mu_tilde,
+                                            mean_function=mean_function,
+                                            Y_metadata=Y_metadata,
+                                            precision=tau_tilde,
+                                            Lm=Lm, dL_dKmm=dL_dKmm,
+                                            psi0=psi0, psi1=psi1, psi2=psi2)
+
+    def expectation_propagation(self, Kmm, Kmn, Y, likelihood, Y_metadata):
+        num_data, output_dim = Y.shape
+        assert output_dim == 1, "This EP methods only works for 1D outputs"
+
+        LLT0 = Kmm.copy()
+        #diag.add(LLT0, 1e-8)
+
+        Lm = jitchol(LLT0)
+        Lmi = dtrtri(Lm)
+        Kmmi = np.dot(Lmi.T,Lmi)
+        KmmiKmn = np.dot(Kmmi,Kmn)
+        Qnn_diag = np.sum(Kmn*KmmiKmn,-2)
+
+        #Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma)
+        mu = np.zeros(num_data)
+        LLT = Kmm.copy() #Sigma = K.copy()
+        Sigma_diag = Qnn_diag.copy() + 1e-8
+
+        #Initial values - Marginal moments
+        Z_hat = np.zeros(num_data,dtype=np.float64)
+        mu_hat = np.zeros(num_data,dtype=np.float64)
+        sigma2_hat = np.zeros(num_data,dtype=np.float64)
+
+        #initial values - Gaussian factors
+        if self.old_mutilde is None:
+            tau_tilde, mu_tilde, v_tilde = np.zeros((3, num_data))
+        else:
+            assert self.old_mutilde.size == num_data, "data size mis-match: did you change the data? try resetting!"
+            mu_tilde, v_tilde = self.old_mutilde, self.old_vtilde
+            tau_tilde = v_tilde/mu_tilde
+
+        #Approximation
+        tau_diff = self.epsilon + 1.
+        v_diff = self.epsilon + 1.
+        iterations = 0
+        tau_tilde_old = 0.
+        v_tilde_old = 0.
+        update_order = np.random.permutation(num_data)
+
+        while (tau_diff > self.epsilon) or (v_diff > self.epsilon):
+            for i in update_order:
+                #Cavity distribution parameters
+                tau_cav = 1./Sigma_diag[i] - self.eta*tau_tilde[i]
+                v_cav = mu[i]/Sigma_diag[i] - self.eta*v_tilde[i]
+                #Marginal moments
+                Z_hat[i], mu_hat[i], sigma2_hat[i] = likelihood.moments_match_ep(Y[i], tau_cav, v_cav)#, Y_metadata=None)#=(None if Y_metadata is None else Y_metadata[i]))
+                #Site parameters update
+                delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i])
+                delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i])
+                tau_tilde[i] += delta_tau
+                v_tilde[i] += delta_v
+                #Posterior distribution parameters update
+
+                #DSYR(Sigma, Sigma[:,i].copy(), -delta_tau/(1.+ delta_tau*Sigma[i,i]))
+                DSYR(LLT,Kmn[:,i].copy(),delta_tau)
+                L = jitchol(LLT+np.eye(LLT.shape[0])*1e-7)
+
+                V,info = dtrtrs(L,Kmn,lower=1)
+                Sigma_diag = np.sum(V*V,-2)
+                si = np.sum(V.T*V[:,i],-1)
+                mu += (delta_v-delta_tau*mu[i])*si
+                #mu = np.dot(Sigma, v_tilde)
+
+            #(re) compute Sigma and mu using full Cholesky decompy
+            LLT = LLT0 + np.dot(Kmn*tau_tilde[None,:],Kmn.T)
+            #diag.add(LLT, 1e-8)
+            L = jitchol(LLT)
+            V, _ = dtrtrs(L,Kmn,lower=1)
+            V2, _ = dtrtrs(L.T,V,lower=0)
+            #Sigma_diag = np.sum(V*V,-2)
+            #Knmv_tilde = np.dot(Kmn,v_tilde)
+            #mu = np.dot(V2.T,Knmv_tilde)
+            Sigma = np.dot(V2.T,V2)
+            mu = np.dot(Sigma,v_tilde)
+
+            #monitor convergence
+            #if iterations>0:
+            tau_diff = np.mean(np.square(tau_tilde-tau_tilde_old))
+            v_diff = np.mean(np.square(v_tilde-v_tilde_old))
+
+            tau_tilde_old = tau_tilde.copy()
+            v_tilde_old = v_tilde.copy()
+
+            # Only to while loop once:?
+            tau_diff = 0
+            v_diff = 0
+            iterations += 1
+
+        mu_tilde = v_tilde/tau_tilde
+        return mu, Sigma, ObsAr(mu_tilde[:,None]), tau_tilde, Z_hat
+
diff --git a/GPy/inference/latent_function_inference/expectation_propagation_dtc.py b/GPy/inference/latent_function_inference/expectation_propagation_dtc.py
deleted file mode 100644
index 0f141824..00000000
--- a/GPy/inference/latent_function_inference/expectation_propagation_dtc.py
+++ /dev/null
@@ -1,142 +0,0 @@
-# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt).
-# Licensed under the BSD 3-clause license (see LICENSE.txt)
-
-import numpy as np
-from ...util import diag
-from ...util.linalg import jitchol, dtrtrs, dtrtri, DSYR
-from ...core.parameterization.observable_array import ObsAr
-from . import VarDTC
-log_2_pi = np.log(2*np.pi)
-
-class EPDTC(VarDTC):
-    const_jitter = 1e-6
-    def __init__(self, epsilon=1e-6, eta=1., delta=1., limit=1):
-        super(EPDTC, self).__init__(limit=limit)
-        self.epsilon, self.eta, self.delta = epsilon, eta, delta
-        self.reset()
-
-    def on_optimization_start(self):
-        self._ep_approximation = None
-
-    def on_optimization_end(self):
-        # TODO: update approximation in the end as well? Maybe even with a switch?
-        pass
-
-    def reset(self):
-        self.old_mutilde, self.old_vtilde = None, None
-        self._ep_approximation = None
-
-    def inference(self, kern, X, Z, likelihood, Y, mean_function=None, Y_metadata=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
-        assert Y.shape[1]==1, "ep in 1D only (for now!)"
-
-        Kmm = kern.K(Z)
-        if psi1 is None:
-            try:
-                Kmn = kern.K(Z, X)
-            except TypeError:
-                Kmn = kern.psi1(Z, X).T
-        else:
-            Kmn = psi1.T
-
-        if self._ep_approximation is None:
-            mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation = self.expectation_propagation(Kmm, Kmn, Y, likelihood, Y_metadata)
-        else:
-            mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation
-
-        return super(EPDTC, self).inference(kern, X, Z, likelihood, mu_tilde,
-                                            mean_function=mean_function,
-                                            Y_metadata=Y_metadata,
-                                            precision=tau_tilde,
-                                            Lm=Lm, dL_dKmm=dL_dKmm,
-                                            psi0=psi0, psi1=psi1, psi2=psi2)
-
-    def expectation_propagation(self, Kmm, Kmn, Y, likelihood, Y_metadata):
-        num_data, output_dim = Y.shape
-        assert output_dim == 1, "This EP methods only works for 1D outputs"
-
-        LLT0 = Kmm.copy()
-        #diag.add(LLT0, 1e-8)
-
-        Lm = jitchol(LLT0)
-        Lmi = dtrtri(Lm)
-        Kmmi = np.dot(Lmi.T,Lmi)
-        KmmiKmn = np.dot(Kmmi,Kmn)
-        Qnn_diag = np.sum(Kmn*KmmiKmn,-2)
-
-        #Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma)
-        mu = np.zeros(num_data)
-        LLT = Kmm.copy() #Sigma = K.copy()
-        Sigma_diag = Qnn_diag.copy() + 1e-8
-
-        #Initial values - Marginal moments
-        Z_hat = np.zeros(num_data,dtype=np.float64)
-        mu_hat = np.zeros(num_data,dtype=np.float64)
-        sigma2_hat = np.zeros(num_data,dtype=np.float64)
-
-        #initial values - Gaussian factors
-        if self.old_mutilde is None:
-            tau_tilde, mu_tilde, v_tilde = np.zeros((3, num_data))
-        else:
-            assert self.old_mutilde.size == num_data, "data size mis-match: did you change the data? try resetting!"
-            mu_tilde, v_tilde = self.old_mutilde, self.old_vtilde
-            tau_tilde = v_tilde/mu_tilde
-
-        #Approximation
-        tau_diff = self.epsilon + 1.
-        v_diff = self.epsilon + 1.
-        iterations = 0
-        tau_tilde_old = 0.
-        v_tilde_old = 0.
-        update_order = np.random.permutation(num_data)
-
-        while (tau_diff > self.epsilon) or (v_diff > self.epsilon):
-            for i in update_order:
-                #Cavity distribution parameters
-                tau_cav = 1./Sigma_diag[i] - self.eta*tau_tilde[i]
-                v_cav = mu[i]/Sigma_diag[i] - self.eta*v_tilde[i]
-                #Marginal moments
-                Z_hat[i], mu_hat[i], sigma2_hat[i] = likelihood.moments_match_ep(Y[i], tau_cav, v_cav)#, Y_metadata=None)#=(None if Y_metadata is None else Y_metadata[i]))
-                #Site parameters update
-                delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i])
-                delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i])
-                tau_tilde[i] += delta_tau
-                v_tilde[i] += delta_v
-                #Posterior distribution parameters update
-
-                #DSYR(Sigma, Sigma[:,i].copy(), -delta_tau/(1.+ delta_tau*Sigma[i,i]))
-                DSYR(LLT,Kmn[:,i].copy(),delta_tau)
-                L = jitchol(LLT+np.eye(LLT.shape[0])*1e-7)
-
-                V,info = dtrtrs(L,Kmn,lower=1)
-                Sigma_diag = np.sum(V*V,-2)
-                si = np.sum(V.T*V[:,i],-1)
-                mu += (delta_v-delta_tau*mu[i])*si
-                #mu = np.dot(Sigma, v_tilde)
-
-            #(re) compute Sigma and mu using full Cholesky decompy
-            LLT = LLT0 + np.dot(Kmn*tau_tilde[None,:],Kmn.T)
-            #diag.add(LLT, 1e-8)
-            L = jitchol(LLT)
-            V, _ = dtrtrs(L,Kmn,lower=1)
-            V2, _ = dtrtrs(L.T,V,lower=0)
-            #Sigma_diag = np.sum(V*V,-2)
-            #Knmv_tilde = np.dot(Kmn,v_tilde)
-            #mu = np.dot(V2.T,Knmv_tilde)
-            Sigma = np.dot(V2.T,V2)
-            mu = np.dot(Sigma,v_tilde)
-
-            #monitor convergence
-            #if iterations>0:
-            tau_diff = np.mean(np.square(tau_tilde-tau_tilde_old))
-            v_diff = np.mean(np.square(v_tilde-v_tilde_old))
-
-            tau_tilde_old = tau_tilde.copy()
-            v_tilde_old = v_tilde.copy()
-
-            # Only to while loop once:?
-            tau_diff = 0
-            v_diff = 0
-            iterations += 1
-
-        mu_tilde = v_tilde/tau_tilde
-        return mu, Sigma, ObsAr(mu_tilde[:,None]), tau_tilde, Z_hat
diff --git a/GPy/models/sparse_gp_classification.py b/GPy/models/sparse_gp_classification.py
index a3e43cf8..e1c468d1 100644
--- a/GPy/models/sparse_gp_classification.py
+++ b/GPy/models/sparse_gp_classification.py
@@ -6,8 +6,7 @@ import numpy as np
 from ..core import SparseGP
 from .. import likelihoods
 from .. import kern
-from ..likelihoods import likelihood
-from ..inference.latent_function_inference import expectation_propagation_dtc
+from ..inference.latent_function_inference import EPDTC
 
 class SparseGPClassification(SparseGP):
     """
@@ -39,7 +38,7 @@ class SparseGPClassification(SparseGP):
         else:
             assert Z.shape[1] == X.shape[1]
 
-        SparseGP.__init__(self, X, Y, Z, kernel, likelihood, inference_method=expectation_propagation_dtc.EPDTC(), name='SparseGPClassification',Y_metadata=Y_metadata)
+        SparseGP.__init__(self, X, Y, Z, kernel, likelihood, inference_method=EPDTC(), name='SparseGPClassification',Y_metadata=Y_metadata)
 
 class SparseGPClassificationUncertainInput(SparseGP):
     """
@@ -78,7 +77,7 @@ class SparseGPClassificationUncertainInput(SparseGP):
         X = NormalPosterior(X, X_variance)
 
         SparseGP.__init__(self, X, Y, Z, kernel, likelihood,
-                          inference_method=expectation_propagation_dtc.EPDTC(),
+                          inference_method=EPDTC(),
                           name='SparseGPClassification', Y_metadata=Y_metadata, normalizer=normalizer)
 
     def parameters_changed(self):

From bf552a09f7ba1fff686203aec1e28e09463e95ea Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 13:03:52 +0100
Subject: [PATCH 06/22] Dapid's travis changes

There was a conflict and I only had access to the web interface.
---
 .travis.yml | 58 ++++++++++++++++++++++++++++++++---------------------
 1 file changed, 35 insertions(+), 23 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index a866cb5a..efe285e7 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,27 +1,39 @@
-language: python
-python:
-  - "2.7"
+sudo: false
+
+language: python
+
+addons:
+  apt:
+    packages:
+      - gfortran
+      - libatlas-dev
+      - libatlas-base-dev
+      - liblapack-dev
+
+python:
+  - 2.7
+  - 3.3
+  - 3.4
 
-# command to install dependencies, e.g. pip install -r requirements.txt --use-mirrors
 before_install:
-  #Install a mini version of anaconda such that we can easily install our dependencies
-  - wget http://repo.continuum.io/miniconda/Miniconda-latest-Linux-x86_64.sh -O miniconda.sh
-  - chmod +x miniconda.sh
-  - ./miniconda.sh -b
-  - export PATH=/home/travis/miniconda/bin:$PATH
-  - conda update --yes conda
-  # Workaround for a permissions issue with Travis virtual machine images
-  # that breaks Python's multiprocessing:
-  # https://github.com/travis-ci/travis-cookbooks/issues/155
-  - sudo rm -rf /dev/shm
-  - sudo ln -s /run/shm /dev/shm
+  - uname -a
+  - free -m
+  - df -h
+  - ulimit -a
+  - pip install -U pip wheel setuptools
+  - pip install numpy cython nose six matplotlib
+  - pip install -v -U scipy
+  - python -V
 
 install:
-  - conda install --yes python=$TRAVIS_PYTHON_VERSION atlas numpy=1.9 scipy=0.16 matplotlib nose sphinx pip nose
-  #- pip install . 
-  - python setup.py build_ext --inplace
-  #--use-mirrors
-  #
-# command to run tests, e.g. python setup.py test
-script: 
-  - nosetests GPy/testing
+  - pip install .
+
+script:
+  - cd $HOME
+  - mkdir empty
+  - cd empty
+  - nosetests GPy
+
+cache:
+  directories:
+    - $HOME/.cache/pip

From 4e479d9db3ab1bbfc5d55f26e200dadaa51a0b23 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 13:08:57 +0100
Subject: [PATCH 07/22] Update .travis.yml

---
 .travis.yml | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index efe285e7..2de17d22 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,5 +1,9 @@
 sudo: false
 
+os:
+  - linux
+  - osx
+  
 language: python
 
 addons:
@@ -21,7 +25,7 @@ before_install:
   - df -h
   - ulimit -a
   - pip install -U pip wheel setuptools
-  - pip install numpy cython nose six matplotlib
+  - pip install numpy nose six
   - pip install -v -U scipy
   - python -V
 

From b4d76fc330f4e22f304d41a616d176f02f3fbb11 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 13:50:34 +0100
Subject: [PATCH 08/22] Update .travis.yml

---
 .travis.yml | 18 ++++++++----------
 1 file changed, 8 insertions(+), 10 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 2de17d22..46879f49 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -16,20 +16,18 @@ addons:
 
 python:
   - 2.7
-  - 3.3
+#  - 3.3
   - 3.4
 
 before_install:
-  - uname -a
-  - free -m
-  - df -h
-  - ulimit -a
-  - pip install -U pip wheel setuptools
-  - pip install numpy nose six
-  - pip install -v -U scipy
-  - python -V
-
+  - wget http://repo.continuum.io/miniconda/Miniconda-latest-Linux-x86_64.sh -O miniconda.sh
+  - chmod +x miniconda.sh
+  - ./miniconda.sh -b
+  - export PATH=/home/travis/miniconda/bin:$PATH
+  - conda update --yes conda
+  
 install:
+  - conda install --yes python=$TRAVIS_PYTHON_VERSION atlas numpy=1.9 scipy=0.16 matplotlib nose sphinx pip nose
   - pip install .
 
 script:

From 5e1ff63d6e29dee466c35a8cc62513c70de314fc Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 13:55:10 +0100
Subject: [PATCH 09/22] Update .travis.yml

---
 .travis.yml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 46879f49..ce2733b0 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -2,8 +2,8 @@ sudo: false
 
 os:
   - linux
-  - osx
-  
+#  - osx
+
 language: python
 
 addons:

From 85a96de17eb634a16de23557b211ee1a0b73c62f Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 13:56:04 +0100
Subject: [PATCH 10/22] Update __init__.py

---
 GPy/plotting/matplot_dep/__init__.py | 30 ++++++++++++++--------------
 1 file changed, 15 insertions(+), 15 deletions(-)

diff --git a/GPy/plotting/matplot_dep/__init__.py b/GPy/plotting/matplot_dep/__init__.py
index a60b52c2..eb33ccfe 100644
--- a/GPy/plotting/matplot_dep/__init__.py
+++ b/GPy/plotting/matplot_dep/__init__.py
@@ -1,18 +1,18 @@
 # Copyright (c) 2014, GPy authors (see AUTHORS.txt).
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 
-import base_plots
-import models_plots
-import priors_plots
-import variational_plots
-import kernel_plots
-import dim_reduction_plots
-import mapping_plots
-import Tango
-import visualize
-import latent_space_visualizations
-import netpbmfile
-import inference_plots
-import maps
-import img_plots
-from ssgplvm import SSGPLVM_plot   
\ No newline at end of file
+import .base_plots
+import .models_plots
+import .priors_plots
+import .variational_plots
+import .kernel_plots
+import .dim_reduction_plots
+import .mapping_plots
+import .Tango
+import .visualize
+import .latent_space_visualizations
+import .netpbmfile
+import .inference_plots
+import .maps
+import .img_plots
+from .ssgplvm import SSGPLVM_plot   

From 7ef32f461569fa5dbc7220cb343acb55bd512f1b Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 13:59:16 +0100
Subject: [PATCH 11/22] Update __init__.py

---
 GPy/plotting/matplot_dep/__init__.py | 28 ++++++++++++++--------------
 1 file changed, 14 insertions(+), 14 deletions(-)

diff --git a/GPy/plotting/matplot_dep/__init__.py b/GPy/plotting/matplot_dep/__init__.py
index eb33ccfe..a72e448f 100644
--- a/GPy/plotting/matplot_dep/__init__.py
+++ b/GPy/plotting/matplot_dep/__init__.py
@@ -1,18 +1,18 @@
 # Copyright (c) 2014, GPy authors (see AUTHORS.txt).
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 
-import .base_plots
-import .models_plots
-import .priors_plots
-import .variational_plots
-import .kernel_plots
-import .dim_reduction_plots
-import .mapping_plots
-import .Tango
-import .visualize
-import .latent_space_visualizations
-import .netpbmfile
-import .inference_plots
-import .maps
-import .img_plots
+from . import base_plots
+from . import models_plots
+from . import priors_plots
+from . import variational_plots
+from . import kernel_plots
+from . import dim_reduction_plots
+from . import mapping_plots
+from . import Tango
+from . import visualize
+from . import latent_space_visualizations
+from . import netpbmfile
+from . import inference_plots
+from . import maps
+from . import img_plots
 from .ssgplvm import SSGPLVM_plot   

From 67e81ed1228b2b5345a33cb4b729c8f2288e3910 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 13:59:56 +0100
Subject: [PATCH 12/22] Update .travis.yml

---
 .travis.yml | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index ce2733b0..0b520aaf 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -6,13 +6,13 @@ os:
 
 language: python
 
-addons:
-  apt:
-    packages:
-      - gfortran
-      - libatlas-dev
-      - libatlas-base-dev
-      - liblapack-dev
+#addons:
+#  apt:
+#    packages:
+#      - gfortran
+#      - libatlas-dev
+#      - libatlas-base-dev
+#      - liblapack-dev
 
 python:
   - 2.7

From 5e5dc0eac5e1aba1d3f419e4bd9f6ffb9f375d95 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 14:21:01 +0100
Subject: [PATCH 13/22] Update base_plots.py

---
 GPy/plotting/matplot_dep/base_plots.py | 9 +--------
 1 file changed, 1 insertion(+), 8 deletions(-)

diff --git a/GPy/plotting/matplot_dep/base_plots.py b/GPy/plotting/matplot_dep/base_plots.py
index 45597628..aefb3e8d 100644
--- a/GPy/plotting/matplot_dep/base_plots.py
+++ b/GPy/plotting/matplot_dep/base_plots.py
@@ -1,13 +1,6 @@
 # #Copyright (c) 2012, GPy authors (see AUTHORS.txt).
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
-
-
-try:
-    #import Tango
-    from matplotlib import pyplot as pb
-except:
-    pass
-import numpy as np
+from matplotlib import pyplot as pb
 
 def ax_default(fignum, ax):
     if ax is None:

From d876847d69d6333c4117bb1c32a53b6190d8ed68 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 14:21:29 +0100
Subject: [PATCH 14/22] Update __init__.py

---
 GPy/plotting/__init__.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/GPy/plotting/__init__.py b/GPy/plotting/__init__.py
index 7172543d..d89369ad 100644
--- a/GPy/plotting/__init__.py
+++ b/GPy/plotting/__init__.py
@@ -2,10 +2,11 @@
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 
 try:
+    import matplotlib
     from . import matplot_dep
 except (ImportError, NameError):
     # Matplotlib not available
     import warnings
     warnings.warn(ImportWarning("Matplotlib not available, install newest version of Matplotlib for plotting"))
     #sys.modules['matplotlib'] =
-    #sys.modules[__name__+'.matplot_dep'] = ImportWarning("Matplotlib not available, install newest version of Matplotlib for plotting")
\ No newline at end of file
+    #sys.modules[__name__+'.matplot_dep'] = ImportWarning("Matplotlib not available, install newest version of Matplotlib for plotting")

From 5bc2370363eecddb9238e485d59e9507f83f26e1 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 14:23:08 +0100
Subject: [PATCH 15/22] Update .travis.yml

---
 .travis.yml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 0b520aaf..6def2656 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -24,10 +24,10 @@ before_install:
   - chmod +x miniconda.sh
   - ./miniconda.sh -b
   - export PATH=/home/travis/miniconda/bin:$PATH
-  - conda update --yes conda
+#  - conda update --yes conda
   
 install:
-  - conda install --yes python=$TRAVIS_PYTHON_VERSION atlas numpy=1.9 scipy=0.16 matplotlib nose sphinx pip nose
+  - conda install --yes python=$TRAVIS_PYTHON_VERSION atlas numpy=1.9 scipy=0.16 matplotlib nose pip six
   - pip install .
 
 script:

From 568984e7a6db7ff9b0d13dc15f16ff9af9028b36 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 14:26:42 +0100
Subject: [PATCH 16/22] Update .travis.yml

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 6def2656..642968ef 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -34,7 +34,7 @@ script:
   - cd $HOME
   - mkdir empty
   - cd empty
-  - nosetests GPy
+  - nosetests GPy.testing
 
 cache:
   directories:

From 72b3be57d710a0b93826990de56856f58a2161f5 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 14:28:52 +0100
Subject: [PATCH 17/22] Update .travis.yml

---
 .travis.yml | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 642968ef..13db69b2 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -2,7 +2,7 @@ sudo: false
 
 os:
   - linux
-#  - osx
+  - osx
 
 language: python
 
@@ -16,7 +16,7 @@ language: python
 
 python:
   - 2.7
-#  - 3.3
+  - 3.3
   - 3.4
 
 before_install:
@@ -27,7 +27,7 @@ before_install:
 #  - conda update --yes conda
   
 install:
-  - conda install --yes python=$TRAVIS_PYTHON_VERSION atlas numpy=1.9 scipy=0.16 matplotlib nose pip six
+  - conda install --yes python=$TRAVIS_PYTHON_VERSION numpy=1.9 scipy=0.16 nose pip six
   - pip install .
 
 script:

From 03c14d5b6cf6408d069da7a73e77e7c806e5a706 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 14:32:47 +0100
Subject: [PATCH 18/22] Update .travis.yml

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 13db69b2..4644dbf1 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -2,7 +2,7 @@ sudo: false
 
 os:
   - linux
-  - osx
+#  - osx
 
 language: python
 

From e65db81a564ca87aa62ac3deee6b916860bc649e Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 14:35:43 +0100
Subject: [PATCH 19/22] Update rv_transformation_tests.py

---
 GPy/testing/rv_transformation_tests.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/GPy/testing/rv_transformation_tests.py b/GPy/testing/rv_transformation_tests.py
index 44d8710d..cfc4c49b 100644
--- a/GPy/testing/rv_transformation_tests.py
+++ b/GPy/testing/rv_transformation_tests.py
@@ -34,7 +34,7 @@ class RVTransformationTestCase(unittest.TestCase):
         # The PDF of the transformed variables
         p_phi = lambda phi : np.exp(-m._objective_grads(phi)[0])
         # To the empirical PDF of:
-        theta_s = prior.rvs(100000)
+        theta_s = prior.rvs(5)
         phi_s = trans.finv(theta_s)
         # which is essentially a kernel density estimation
         kde = st.gaussian_kde(phi_s)
@@ -56,7 +56,7 @@ class RVTransformationTestCase(unittest.TestCase):
         # The following test cannot be very accurate
         self.assertTrue(np.linalg.norm(pdf_phi - kde(phi)) / np.linalg.norm(kde(phi)) <= 1e-1)
         # Check the gradients at a few random points
-        for i in range(10):
+        for i in range(len(theta_s)):
             m.theta = theta_s[i]
             self.assertTrue(m.checkgrad(verbose=True))
 

From a3f0570e00918e692b1cdfb70ae2a779aee77603 Mon Sep 17 00:00:00 2001
From: Max Zwiessele <ibinbei@gmail.com>
Date: Sat, 12 Sep 2015 14:41:39 +0100
Subject: [PATCH 20/22] Update rv_transformation_tests.py

---
 GPy/testing/rv_transformation_tests.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/GPy/testing/rv_transformation_tests.py b/GPy/testing/rv_transformation_tests.py
index cfc4c49b..18dccd36 100644
--- a/GPy/testing/rv_transformation_tests.py
+++ b/GPy/testing/rv_transformation_tests.py
@@ -34,7 +34,7 @@ class RVTransformationTestCase(unittest.TestCase):
         # The PDF of the transformed variables
         p_phi = lambda phi : np.exp(-m._objective_grads(phi)[0])
         # To the empirical PDF of:
-        theta_s = prior.rvs(5)
+        theta_s = prior.rvs(1e6)
         phi_s = trans.finv(theta_s)
         # which is essentially a kernel density estimation
         kde = st.gaussian_kde(phi_s)
@@ -56,7 +56,7 @@ class RVTransformationTestCase(unittest.TestCase):
         # The following test cannot be very accurate
         self.assertTrue(np.linalg.norm(pdf_phi - kde(phi)) / np.linalg.norm(kde(phi)) <= 1e-1)
         # Check the gradients at a few random points
-        for i in range(len(theta_s)):
+        for i in range(5):
             m.theta = theta_s[i]
             self.assertTrue(m.checkgrad(verbose=True))
 

From f71b57c24ed86e73c3661aa72b63b0236f70b316 Mon Sep 17 00:00:00 2001
From: Alan Saul <alan.daniel.saul@gmail.com>
Date: Mon, 14 Sep 2015 14:38:50 +0100
Subject: [PATCH 21/22] Missing numpy import

---
 GPy/plotting/matplot_dep/base_plots.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/GPy/plotting/matplot_dep/base_plots.py b/GPy/plotting/matplot_dep/base_plots.py
index aefb3e8d..7ee0bd37 100644
--- a/GPy/plotting/matplot_dep/base_plots.py
+++ b/GPy/plotting/matplot_dep/base_plots.py
@@ -1,6 +1,7 @@
 # #Copyright (c) 2012, GPy authors (see AUTHORS.txt).
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 from matplotlib import pyplot as pb
+import numpy as np
 
 def ax_default(fignum, ax):
     if ax is None:

From 09571e92648bc8bef16ceeaafe7d5c9a676bb6b0 Mon Sep 17 00:00:00 2001
From: Zhenwen Dai <z.dai@sheffield.ac.uk>
Date: Fri, 18 Sep 2015 13:41:45 +0100
Subject: [PATCH 22/22] add adadelta as an optimizer

---
 GPy/core/model.py                          |  2 +-
 GPy/inference/optimization/optimization.py | 24 +++++++++++++++++++++-
 2 files changed, 24 insertions(+), 2 deletions(-)

diff --git a/GPy/core/model.py b/GPy/core/model.py
index 9d8b89f4..8c00667e 100644
--- a/GPy/core/model.py
+++ b/GPy/core/model.py
@@ -255,7 +255,7 @@ class Model(Parameterized):
             opt.model = self
         else:
             optimizer = optimization.get_optimizer(optimizer)
-            opt = optimizer(start, model=self, max_iters=max_iters, **kwargs)
+            opt = optimizer(x_init=start, model=self, max_iters=max_iters, **kwargs)
 
         with VerboseOptimization(self, opt, maxiters=max_iters, verbose=messages, ipython_notebook=ipython_notebook, clear_after_finish=clear_after_finish) as vo:
             opt.run(f_fp=self._objective_grads, f=self._objective, fp=self._grads)
diff --git a/GPy/inference/optimization/optimization.py b/GPy/inference/optimization/optimization.py
index 48bdd809..9aab1bec 100644
--- a/GPy/inference/optimization/optimization.py
+++ b/GPy/inference/optimization/optimization.py
@@ -228,13 +228,35 @@ class opt_SCG(Optimizer):
         self.f_opt = self.trace[-1]
         self.funct_eval = opt_result[2]
         self.status = opt_result[3]
+        
+class Opt_Adadelta(Optimizer):
+    def __init__(self, step_rate=0.1, decay=0.9, momentum=0, *args, **kwargs):
+        Optimizer.__init__(self, *args, **kwargs)
+        self.opt_name = "Adadelta (climin)"
+        self.step_rate=step_rate
+        self.decay = decay
+        self.momentum = momentum
+
+    def opt(self, f_fp=None, f=None, fp=None):
+        assert not fp is None
+        
+        import climin
+                    
+        opt = climin.adadelta.Adadelta(self.x_init, fp, step_rate=self.step_rate, decay=self.decay, momentum=self.momentum)
+        
+        for info in opt:
+            if info['n_iter']>=self.max_iters:
+                self.x_opt =  opt.wrt
+                self.status = 'maximum number of function evaluations exceeded '
+                break
 
 def get_optimizer(f_min):
 
     optimizers = {'fmin_tnc': opt_tnc,
           'simplex': opt_simplex,
           'lbfgsb': opt_lbfgsb,
-          'scg': opt_SCG}
+          'scg': opt_SCG,
+          'adadelta':Opt_Adadelta}
 
     if rasm_available:
         optimizers['rasmussen'] = opt_rasm