diff --git a/GPy/models/sparse_GP_old.py b/GPy/models/sparse_GP_old.py deleted file mode 100644 index 7b043209..00000000 --- a/GPy/models/sparse_GP_old.py +++ /dev/null @@ -1,258 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - -import numpy as np -import pylab as pb -from ..util.linalg import mdot, jitchol, chol_inv, pdinv -from ..util.plot import gpplot -from .. import kern -from GP import GP - - -#Still TODO: -# make use of slices properly (kernel can now do this) -# enable heteroscedatic noise (kernel will need to compute psi2 as a (NxMxM) array) - -class sparse_GP(GP): - """ - Variational sparse GP model (Regression) - - :param X: inputs - :type X: np.ndarray (N x Q) - :param Y: observed data - :type Y: np.ndarray of observations (N x D) - :param kernel : the kernel/covariance function. See link kernels - :type kernel: a GPy kernel - :param Z: inducing inputs (optional, see note) - :type Z: np.ndarray (M x Q) | None - :param X_uncertainty: The uncertainty in the measurements of X (Gaussian variance) - :type X_uncertainty: np.ndarray (N x Q) | None - :param Zslices: slices for the inducing inputs (see slicing TODO: link) - :param M : Number of inducing points (optional, default 10. Ignored if Z is not None) - :type M: int - :param beta: noise precision. TODO> ignore beta if doing EP - :type beta: float - :param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales) - :type normalize_(X|Y): bool - """ - - def __init__(self,X,Y=None,kernel=None,X_uncertainty=None,beta=100.,Z=None,Zslices=None,M=10,normalize_X=False,normalize_Y=False,likelihood=None,method_ep='DTC',epsilon_ep=1e-3,power_ep=[1.,1.]): - - if Z is None: - self.Z = np.random.permutation(X.copy())[:M] - self.M = M - else: - assert Z.shape[1]==X.shape[1] - self.Z = Z - self.M = Z.shape[0] - if X_uncertainty is None: - self.has_uncertain_inputs=False - else: - assert X_uncertainty.shape==X.shape - self.has_uncertain_inputs=True - self.X_uncertainty = X_uncertainty - - 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) - - #normalise X uncertainty also - if self.has_uncertain_inputs: - self.X_uncertainty /= np.square(self._Xstd) - - if not self.EP: - self.trYYT = np.sum(np.square(self.Y)) - else: - self.method_ep = method_ep - - #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.beta = p[self.M*self.Q] - self.kern._set_params(p[self.Z.size + 1:]) - else: - self.kern._set_params(p[self.Z.size:]) - 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 not self.EP: - self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty)#.sum() NOTE psi0 is now a vector - 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) - #self.psi2_beta_scaled = ? - else: - raise NotImplementedError, "uncertain_inputs not yet supported for EP" - 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) - self.psi2_beta_scaled = np.dot(self.psi1,self.beta*self.psi1.T) - - def _computations(self): - # 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.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.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) - self.trace_K_beta_scaled = (self.psi0*self.beta).sum() - np.trace(self.A) - if not self.EP: - self.trace_K = self.psi0.sum() - np.trace(self.A)/self.beta - - # Compute dL_dpsi - self.dL_dpsi1 = mdot(self.LLambdai.T,self.C,self.V.T) - if not self.EP: - self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N) - if self.has_uncertain_inputs: - self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G) - else: - self.dL_dpsi2_ = - 0.5 * (self.D*(self.LBL_inv - self.Kmmi) + self.G) - else: - self.dL_dpsi0 = - 0.5 * self.D * self.beta.flatten() - if not self.has_uncertain_inputs: - self.dL_dpsi2_ = - 0.5 * (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.*mdot(self.LBL_inv, self.psi2_beta_scaled, self.Kmmi) + self.Kmmi) # dC - self.dL_dKmm += np.dot(np.dot(self.G,self.psi2_beta_scaled) - np.dot(self.LBL_inv, self.psi1VVpsi1), self.Kmmi) + 0.5*self.G # dE - - def approximate_likelihood(self): - assert not isinstance(self.likelihood, gaussian), "EP is only available for non-gaussian likelihoods" - if self.method_ep == 'DTC': - self.ep_approx = DTC(self.Kmm,self.likelihood,self.psi1,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta]) - elif self.method_ep == 'FITC': - 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.Y, self.Z_ep = self.ep_approx.fit_EP() - self.trbetaYYT = np.sum(np.square(self.Y)*self.beta) - self._computations() - - def log_likelihood(self): - """ - Compute the (lower bound on the) log marginal likelihood - """ - if not self.EP: - A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta)) - D = -0.5*self.beta*self.trYYT - else: - A = -0.5*self.D*(self.N*np.log(2.*np.pi) - np.sum(np.log(self.beta))) - D = -0.5*self.trbetaYYT - B = -0.5*self.D*self.trace_K_beta_scaled - C = -0.5*self.D * self.B_logdet - E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv) - return A+B+C+D+E - - def dL_dbeta(self): - """ - Compute the gradient of the log likelihood wrt beta. - """ - #TODO: suport heteroscedatic noise - dA_dbeta = 0.5 * self.N*self.D/self.beta - dB_dbeta = - 0.5 * self.D * self.trace_K - dC_dbeta = - 0.5 * self.D * np.sum(self.Bi*self.A)/self.beta - dD_dbeta = - 0.5 * self.trYYT - tmp = mdot(self.LBi.T, self.LLambdai, self.psi1V) - dE_dbeta = (np.sum(np.square(self.C)) - 0.5 * np.sum(self.A * np.dot(tmp, tmp.T)))/self.beta - - return np.squeeze(dA_dbeta + dB_dbeta + dC_dbeta + dD_dbeta + dE_dbeta) - - def dL_dtheta(self): - """ - Compute and return the derivative of the log marginal likelihood wrt the parameters of the kernel - """ - dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm,self.Z) - if self.has_uncertain_inputs: - dL_dtheta += self.kern.dpsi0_dtheta(self.dL_dpsi0, self.Z,self.X,self.X_uncertainty) - dL_dtheta += self.kern.dpsi1_dtheta(self.dL_dpsi1.T,self.Z,self.X, self.X_uncertainty) - dL_dtheta += self.kern.dpsi2_dtheta(self.dL_dpsi2,self.Z,self.X, self.X_uncertainty) # for multiple_beta, dL_dpsi2 will be a different shape - else: - #re-cast computations in psi2 back to psi1: - dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2_,self.beta.T*self.psi1) #dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1) - dL_dtheta += self.kern.dK_dtheta(dL_dpsi1,self.Z,self.X) - dL_dtheta += self.kern.dKdiag_dtheta(self.dL_dpsi0, self.X) - - return dL_dtheta - - def dL_dZ(self): - """ - The derivative of the bound wrt the inducing inputs Z - """ - dL_dZ = 2.*self.kern.dK_dX(self.dL_dKmm,self.Z,)#factor of two becase of vertical and horizontal 'stripes' in dKmm_dZ - if self.has_uncertain_inputs: - dL_dZ += self.kern.dpsi1_dZ(self.dL_dpsi1.T,self.Z,self.X, self.X_uncertainty) - dL_dZ += self.kern.dpsi2_dZ(self.dL_dpsi2,self.Z,self.X, self.X_uncertainty) - else: - #re-cast computations in psi2 back to psi1: - dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2_,self.beta.T*self.psi1)#dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1) - dL_dZ += self.kern.dK_dX(dL_dpsi1,self.Z,self.X) - return dL_dZ - - def _log_likelihood_gradients(self): - if not self.EP: - return np.hstack([self.dL_dZ().flatten(), self.dL_dbeta(), self.dL_dtheta()]) - else: - return np.hstack([self.dL_dZ().flatten(), self.dL_dtheta()]) - - def _raw_predict(self, Xnew, slices, full_cov=False): - """Internal helper function for making predictions, does not account for normalisation""" - Kx = self.kern.K(self.Z, Xnew) - mu = mdot(Kx.T, self.LBL_inv, self.psi1V) - phi = None - if full_cov: - Kxx = self.kern.K(Xnew) - var = Kxx - mdot(Kx.T, (self.Kmmi - self.LBL_inv), Kx) - if not self.EP: - var += np.eye(Xnew.shape[0])/self.beta - else: - raise NotImplementedError, "full_cov = True not implemented for EP" - else: - Kxx = self.kern.Kdiag(Xnew) - var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.LBL_inv, Kx),0) - if not self.EP: - var += 1./self.beta - else: - phi = self.likelihood.predictive_mean(mu,var) - return mu,var,phi - - def plot(self, *args, **kwargs): - """ - Plot the fitted model: just call the GP_regression plot function and then add inducing inputs - """ - GP.plot(self,*args,**kwargs) - if self.Q==1: - pb.plot(self.Z,self.Z*0+pb.ylim()[0],'k|',mew=1.5,markersize=12) - if self.has_uncertain_inputs: - pb.errorbar(self.X[:,0], pb.ylim()[0]+np.zeros(self.N), xerr=2*np.sqrt(self.X_uncertainty.flatten())) - if self.Q==2: - pb.plot(self.Z[:,0],self.Z[:,1],'wo')