diff --git a/GPy/models/GP.py b/GPy/models/GP.py index 95145978..4d80ab87 100644 --- a/GPy/models/GP.py +++ b/GPy/models/GP.py @@ -73,7 +73,6 @@ class GP(model): self.EP = False self.Y = Y self.beta = 100.#FIXME beta should be an explicit parameter for this model - # Here's some simple normalisation if normalize_Y: self._Ymean = Y.mean(0)[None,:] @@ -88,8 +87,9 @@ class GP(model): self.YYT = np.dot(self.Y, self.Y.T) else: self.YYT = None - else: + if self.D > 1: + raise NotImplementedError, "EP is not implemented for D > 1" # Y is defined after approximating the likelihood self.EP = True self.eta,self.delta = power_ep diff --git a/GPy/models/sparse_GP.py b/GPy/models/sparse_GP.py index f5381eed..ea1ba100 100644 --- a/GPy/models/sparse_GP.py +++ b/GPy/models/sparse_GP.py @@ -60,48 +60,52 @@ class sparse_GP(GP): 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) self.trYYT = np.sum(np.square(self.Y)) if not self.EP else None - #normalise X uncertainty also if self.has_uncertain_inputs: self.X_uncertainty /= np.square(self._Xstd) def _set_params(self, p): + self.Z = p[:self.M*self.Q].reshape(self.M, self.Q) if not self.EP: - self.Z = p[:self.M*self.Q].reshape(self.M, self.Q) - self.beta = p[self.M*self.Q] + #self.beta = p[self.M*self.Q] + self.beta = np.repeat(p[self.M*self.Q],self.N)[:,None] self.kern._set_params(p[self.Z.size + 1:]) self.beta2 = self.beta**2 - self._compute_kernel_matrices() - self._computations() else: - self.Z = p[:self.M*self.Q].reshape(self.M, self.Q) self.kern._set_params(p[self.Z.size:]) - #self._compute_kernel_matrices() this is replaced by _ep_kernel_matrices - self._ep_kernel_matrices() - self._ep_computations() + if self.Y is None: + self.Y = np.ones([self.N,1]) + self._compute_kernel_matrices() + self._computations() + + def _get_params(self): + if not self.EP: + return np.hstack([self.Z.flatten(),self.beta,self.kern._get_params_transformed()]) + else: + return np.hstack([self.Z.flatten(),self.kern._get_params_transformed()]) + + def _get_param_names(self): + if not self.EP: + 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() + else: + 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() def _compute_kernel_matrices(self): # kernel computations, using BGPLVM notation #TODO: slices for psi statistics (easy enough) - self.Kmm = self.kern.K(self.Z) if self.has_uncertain_inputs: - if self.hetero_noise: - raise NotImplementedError, "uncertain ips and het noise not yet supported" - else: - self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum() + if not self.EP: + self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty)#.sum() self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T - self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty) - else: - if self.hetero_noise: - print "rick's stuff here" - - - + self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)#FIXME add beta vector else: - self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices).sum() - self.psi1 = self.kern.K(self.Z,self.X) - self.psi2 = np.dot(self.psi1,self.psi1.T) + raise NotImplementedError, "uncertain_inputs not yet supported for EP" + else: + self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices)#.sum() FIXME + self.psi1 = self.kern.K(self.Z,self.X) + self.psi2 = np.dot(self.psi1,self.psi1.T) + self.psi2_beta_scaled = np.dot(self.psi1,self.beta*self.psi1.T) def _computations(self): # TODO find routine to multiply triangular matrices @@ -109,17 +113,17 @@ class sparse_GP(GP): self.psi1V = np.dot(self.psi1, self.V) self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T) self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm) - self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T) + self.A = mdot(self.Lmi, self.psi2_beta_scaled, self.Lmi.T) self.B = np.eye(self.M) + self.A self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B) self.LLambdai = np.dot(self.LBi, self.Lmi) - self.trace_K = self.psi0 - np.trace(self.A)/self.beta + self.trace_K = self.psi0.sum() - np.trace(self.A) self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi) self.C = mdot(self.LLambdai, self.psi1V) self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T) # Compute dL_dpsi - self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N) + self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones([self.N,1]) self.dL_dpsi1 = mdot(self.LLambdai.T,self.C,self.V.T) self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G) @@ -133,76 +137,28 @@ class sparse_GP(GP): if self.ep_proxy == 'DTC': self.ep_approx = DTC(self.Kmm,self.likelihood,self.psi1,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta]) elif self.ep_proxy == 'FITC': - self.Knn_diag = self.kern.psi0(self.Z,self.X, self.X_uncertainty) #TODO psi0 already calculates this - self.ep_approx = FITC(self.Kmm,self.likelihood,self.psi1,self.Knn_diag,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta]) + self.ep_approx = FITC(self.Kmm,self.likelihood,self.psi1,self.psi0,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta]) else: self.ep_approx = Full(self.X,self.likelihood,self.kernel,inducing=None,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta]) - self.beta, self.v_tilde, self.Z_hat, self.tau_, self.v_=self.ep_approx.fit_EP() - self._ep_kernel_matrices() + self.beta, self.Y, self.Z_ep = self.ep_approx.fit_EP() self._computations() - def _ep_kernel_matrices(self): - self.Kmm = self.kern.K(self.Z) - if self.has_uncertain_inputs: - self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum() - self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T - self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty) #FIXME include beta - else: - self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices) - self.psi1 = self.kern.K(self.Z,self.X) - self.psi2 = np.dot(self.psi1,self.psi1.T) - self.psi2_beta_scaled = np.dot(self.psi1,self.beta*self.psi1.T) - - def _ep_computations(self): - # Y: EP likelihood is defined as a regression model for mu_tilde - self.Y = self.v_tilde/self.beta - self._Ymean = np.zeros((1,self.Y.shape[1])) - self._Ystd = np.ones((1,self.Y.shape[1])) - self.trbetaYYT = np.sum(self.beta*np.square(self.Y)) - if self.D > self.N: - # then it's more efficient to store YYT - self.YYT = np.dot(self.Y, self.Y.T) - else: - self.YYT = None - self.mu_ = self.v_/self.tau_ - # TODO find routine to multiply triangular matrices - self.V = self.beta*self.Y - self.psi1V = np.dot(self.psi1, self.V) - self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T) - self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm) - #self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T) - self.A = mdot(self.Lmi, self.psi2_beta_scaled, self.Lmi.T) - self.B = np.eye(self.M) + self.A - self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B) - self.LLambdai = np.dot(self.LBi, self.Lmi) - self.trace_K = self.psi0.sum() - np.trace(self.A) - self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi) - self.C = mdot(self.LLambdai, self.psi1V) - self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T) - - # Compute dL_dpsi - #self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N) - self.dL_dpsi0 = - 0.5 * self.D * self.beta.flatten() * np.ones(self.N) #TODO check - self.dL_dpsi1 = mdot(self.LLambdai.T,self.C,self.V.T) - #self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G) - self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G) - - # Compute dL_dKmm - self.dL_dKmm = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi) # dB - self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi) + self.Kmmi) # dC - 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 - - def _get_params(self): + def log_likelihood(self): + """ + Compute the (lower bound on the) log marginal likelihood + """ if not self.EP: - return np.hstack([self.Z.flatten(),self.beta,self.kern._get_params_transformed()]) + A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta)) else: - return np.hstack([self.Z.flatten(),self.kern._get_params_transformed()]) + A = -0.5*self.D*(self.N*np.log(2.*np.pi) - np.sum(np.log(self.beta))) + B = -0.5*self.D*self.trace_K + C = -0.5*self.D * self.B_logdet + D = -0.5*self.beta*self.trYYT + E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv) + return A+B+C+D+E + + - def _get_param_names(self): - if not self.EP: - 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() - else: - 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() def log_likelihood(self): """