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More changes.
This commit is contained in:
Ricardo Andrade
parent
0a88df62c3
commit
bb1e0021d7
2 changed files with 48 additions and 92 deletions
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@ -73,7 +73,6 @@ class GP(model):
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self.EP = False
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self.Y = Y
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self.beta = 100.#FIXME beta should be an explicit parameter for this model
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# Here's some simple normalisation
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if normalize_Y:
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self._Ymean = Y.mean(0)[None,:]
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@ -88,8 +87,9 @@ class GP(model):
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self.YYT = np.dot(self.Y, self.Y.T)
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else:
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self.YYT = None
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else:
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if self.D > 1:
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raise NotImplementedError, "EP is not implemented for D > 1"
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# Y is defined after approximating the likelihood
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self.EP = True
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self.eta,self.delta = power_ep
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@ -60,48 +60,52 @@ class sparse_GP(GP):
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GP.__init__(self, X=X, Y=Y, kernel=kernel, normalize_X=normalize_X, normalize_Y=normalize_Y,likelihood=likelihood,epsilon_ep=epsilon_ep,power_ep=power_ep)
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self.trYYT = np.sum(np.square(self.Y)) if not self.EP else None
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#normalise X uncertainty also
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if self.has_uncertain_inputs:
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self.X_uncertainty /= np.square(self._Xstd)
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def _set_params(self, p):
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self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
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if not self.EP:
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self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
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self.beta = p[self.M*self.Q]
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#self.beta = p[self.M*self.Q]
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self.beta = np.repeat(p[self.M*self.Q],self.N)[:,None]
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self.kern._set_params(p[self.Z.size + 1:])
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self.beta2 = self.beta**2
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self._compute_kernel_matrices()
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self._computations()
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else:
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self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
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self.kern._set_params(p[self.Z.size:])
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#self._compute_kernel_matrices() this is replaced by _ep_kernel_matrices
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self._ep_kernel_matrices()
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self._ep_computations()
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if self.Y is None:
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self.Y = np.ones([self.N,1])
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self._compute_kernel_matrices()
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self._computations()
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def _get_params(self):
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if not self.EP:
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return np.hstack([self.Z.flatten(),self.beta,self.kern._get_params_transformed()])
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else:
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return np.hstack([self.Z.flatten(),self.kern._get_params_transformed()])
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def _get_param_names(self):
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if not self.EP:
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return sum([['iip_%i_%i'%(i,j) for i in range(self.Z.shape[0])] for j in range(self.Z.shape[1])],[]) + ['noise_precision']+self.kern._get_param_names_transformed()
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else:
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return sum([['iip_%i_%i'%(i,j) for i in range(self.Z.shape[0])] for j in range(self.Z.shape[1])],[]) + self.kern._get_param_names_transformed()
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def _compute_kernel_matrices(self):
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# kernel computations, using BGPLVM notation
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#TODO: slices for psi statistics (easy enough)
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self.Kmm = self.kern.K(self.Z)
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if self.has_uncertain_inputs:
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if self.hetero_noise:
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raise NotImplementedError, "uncertain ips and het noise not yet supported"
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else:
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self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
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if not self.EP:
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self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty)#.sum()
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self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
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self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)
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else:
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if self.hetero_noise:
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print "rick's stuff here"
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self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)#FIXME add beta vector
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else:
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self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices).sum()
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self.psi1 = self.kern.K(self.Z,self.X)
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self.psi2 = np.dot(self.psi1,self.psi1.T)
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raise NotImplementedError, "uncertain_inputs not yet supported for EP"
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else:
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self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices)#.sum() FIXME
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self.psi1 = self.kern.K(self.Z,self.X)
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self.psi2 = np.dot(self.psi1,self.psi1.T)
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self.psi2_beta_scaled = np.dot(self.psi1,self.beta*self.psi1.T)
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def _computations(self):
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# TODO find routine to multiply triangular matrices
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@ -109,17 +113,17 @@ class sparse_GP(GP):
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self.psi1V = np.dot(self.psi1, self.V)
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self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
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self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
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self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T)
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self.A = mdot(self.Lmi, self.psi2_beta_scaled, self.Lmi.T)
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self.B = np.eye(self.M) + self.A
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self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
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self.LLambdai = np.dot(self.LBi, self.Lmi)
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self.trace_K = self.psi0 - np.trace(self.A)/self.beta
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self.trace_K = self.psi0.sum() - np.trace(self.A)
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self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
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self.C = mdot(self.LLambdai, self.psi1V)
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self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
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# Compute dL_dpsi
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self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
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self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones([self.N,1])
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self.dL_dpsi1 = mdot(self.LLambdai.T,self.C,self.V.T)
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self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
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@ -133,76 +137,28 @@ class sparse_GP(GP):
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if self.ep_proxy == 'DTC':
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self.ep_approx = DTC(self.Kmm,self.likelihood,self.psi1,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
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elif self.ep_proxy == 'FITC':
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self.Knn_diag = self.kern.psi0(self.Z,self.X, self.X_uncertainty) #TODO psi0 already calculates this
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self.ep_approx = FITC(self.Kmm,self.likelihood,self.psi1,self.Knn_diag,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
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self.ep_approx = FITC(self.Kmm,self.likelihood,self.psi1,self.psi0,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
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else:
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self.ep_approx = Full(self.X,self.likelihood,self.kernel,inducing=None,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
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self.beta, self.v_tilde, self.Z_hat, self.tau_, self.v_=self.ep_approx.fit_EP()
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self._ep_kernel_matrices()
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self.beta, self.Y, self.Z_ep = self.ep_approx.fit_EP()
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self._computations()
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def _ep_kernel_matrices(self):
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self.Kmm = self.kern.K(self.Z)
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if self.has_uncertain_inputs:
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self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
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self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
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self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty) #FIXME include beta
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else:
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self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices)
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self.psi1 = self.kern.K(self.Z,self.X)
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self.psi2 = np.dot(self.psi1,self.psi1.T)
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self.psi2_beta_scaled = np.dot(self.psi1,self.beta*self.psi1.T)
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def _ep_computations(self):
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# Y: EP likelihood is defined as a regression model for mu_tilde
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self.Y = self.v_tilde/self.beta
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self._Ymean = np.zeros((1,self.Y.shape[1]))
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self._Ystd = np.ones((1,self.Y.shape[1]))
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self.trbetaYYT = np.sum(self.beta*np.square(self.Y))
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if self.D > self.N:
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# then it's more efficient to store YYT
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self.YYT = np.dot(self.Y, self.Y.T)
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else:
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self.YYT = None
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self.mu_ = self.v_/self.tau_
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# TODO find routine to multiply triangular matrices
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self.V = self.beta*self.Y
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self.psi1V = np.dot(self.psi1, self.V)
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self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
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self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
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#self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T)
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self.A = mdot(self.Lmi, self.psi2_beta_scaled, self.Lmi.T)
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self.B = np.eye(self.M) + self.A
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self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
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self.LLambdai = np.dot(self.LBi, self.Lmi)
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self.trace_K = self.psi0.sum() - np.trace(self.A)
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self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
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self.C = mdot(self.LLambdai, self.psi1V)
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self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
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# Compute dL_dpsi
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#self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
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self.dL_dpsi0 = - 0.5 * self.D * self.beta.flatten() * np.ones(self.N) #TODO check
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self.dL_dpsi1 = mdot(self.LLambdai.T,self.C,self.V.T)
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#self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
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self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
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# Compute dL_dKmm
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self.dL_dKmm = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi) # dB
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self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi) + self.Kmmi) # dC
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self.dL_dKmm += np.dot(np.dot(self.G,self.beta*self.psi2) - np.dot(self.LBL_inv, self.psi1VVpsi1), self.Kmmi) + 0.5*self.G # dE
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def _get_params(self):
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def log_likelihood(self):
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"""
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Compute the (lower bound on the) log marginal likelihood
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"""
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if not self.EP:
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return np.hstack([self.Z.flatten(),self.beta,self.kern._get_params_transformed()])
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A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta))
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else:
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return np.hstack([self.Z.flatten(),self.kern._get_params_transformed()])
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A = -0.5*self.D*(self.N*np.log(2.*np.pi) - np.sum(np.log(self.beta)))
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B = -0.5*self.D*self.trace_K
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C = -0.5*self.D * self.B_logdet
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D = -0.5*self.beta*self.trYYT
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E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
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return A+B+C+D+E
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def _get_param_names(self):
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if not self.EP:
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return sum([['iip_%i_%i'%(i,j) for i in range(self.Z.shape[0])] for j in range(self.Z.shape[1])],[]) + ['noise_precision']+self.kern._get_param_names_transformed()
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else:
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return sum([['iip_%i_%i'%(i,j) for i in range(self.Z.shape[0])] for j in range(self.Z.shape[1])],[]) + self.kern._get_param_names_transformed()
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def log_likelihood(self):
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"""
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