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FITC is back
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Ricardo
parent
d238f7709f
commit
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1 changed files with 32 additions and 98 deletions
130
GPy/core/fitc.py
130
GPy/core/fitc.py
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@ -7,14 +7,8 @@ from ..util.linalg import mdot, jitchol, chol_inv, tdot, symmetrify,pdinv
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from ..util.plot import gpplot
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from .. import kern
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from scipy import stats, linalg
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from gp_base import GPBase
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from sparse_gp import SparseGP
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def backsub_both_sides(L,X):
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""" Return L^-T * X * L^-1, assumuing X is symmetrical and L is lower cholesky"""
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tmp,_ = linalg.lapack.flapack.dtrtrs(L,np.asfortranarray(X),lower=1,trans=1)
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return linalg.lapack.flapack.dtrtrs(L,np.asfortranarray(tmp.T),lower=1,trans=1)[0].T
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class FITC(SparseGP):
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"""
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sparse FITC approximation
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@ -27,48 +21,13 @@ class FITC(SparseGP):
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:type kernel: a GPy.kern.kern instance
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:param Z: inducing inputs (optional, see note)
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:type Z: np.ndarray (M x Q) | None
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:param M : Number of inducing points (optional, default 10. Ignored if Z is not None)
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:type M: int
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:param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
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:type normalize_(X|Y): bool
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"""
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def __init__(self, X, likelihood, kernel, Z, normalize_X=False):
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GPBase.__init__(self, X, likelihood, kernel, normalize_X=normalize_X)
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self.Z = Z
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self.M = Z.shape[0]
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self.likelihood = likelihood
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X_variance = None
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if X_variance is None:
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self.has_uncertain_inputs = False
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else:
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assert X_variance.shape == X.shape
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self.has_uncertain_inputs = True
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self.X_variance = X_variance
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if normalize_X:
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self.Z = (self.Z.copy() - self._Xmean) / self._Xstd
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# normalize X uncertainty also
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if self.has_uncertain_inputs:
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self.X_variance /= np.square(self._Xstd)
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def _set_params(self, p):
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self.Z = p[:self.M * self.input_dim].reshape(self.M, self.input_dim)
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self.kern._set_params(p[self.Z.size:self.Z.size + self.kern.Nparam])
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self.likelihood._set_params(p[self.Z.size + self.kern.Nparam:])
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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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return np.hstack([self.Z.flatten(), self.kern._get_params_transformed(), self.likelihood._get_params()])
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def _get_param_names(self):
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return sum([['iip_%i_%i' % (i, j) for j in range(self.Z.shape[1])] for i in range(self.Z.shape[0])],[])\
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+ self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
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SparseGP.__init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False)
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assert self.output_dim == 1, "FITC model is not defined for handling multiple outputs"
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def update_likelihood_approximation(self):
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"""
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@ -77,47 +36,33 @@ class FITC(SparseGP):
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For a Gaussian likelihood, no iteration is required:
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this function does nothing
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"""
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if self.has_uncertain_inputs:
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raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
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else:
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self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
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self._set_params(self._get_params()) # update the GP
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self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
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self._set_params(self._get_params()) # update the GP
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def _compute_kernel_matrices(self):
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# kernel computations, using BGPLVM notation
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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_variance)
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self.psi1 = self.kern.psi1(self.Z, self.X, self.X_variance).T
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self.psi2 = self.kern.psi2(self.Z, self.X, self.X_variance)
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else:
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self.psi0 = self.kern.Kdiag(self.X)
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self.psi1 = self.kern.K(self.Z, self.X)
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self.psi2 = None
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self.psi0 = self.kern.Kdiag(self.X)
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self.psi1 = self.kern.K(self.Z, self.X)
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self.psi2 = None
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def _computations(self):
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#factor Kmm
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self.Lm = jitchol(self.Kmm)
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self.Lmi,info = linalg.lapack.flapack.dtrtrs(self.Lm,np.eye(self.M),lower=1)
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self.Lmi,info = linalg.lapack.flapack.dtrtrs(self.Lm,np.eye(self.num_inducing),lower=1)
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Lmipsi1 = np.dot(self.Lmi,self.psi1)
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self.Qnn = np.dot(Lmipsi1.T,Lmipsi1).copy()
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self.Diag0 = self.psi0 - np.diag(self.Qnn)
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self.beta_star = self.likelihood.precision/(1. + self.likelihood.precision*self.Diag0[:,None]) #Includes Diag0 in the precision
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self.beta_star = self.likelihood.precision/(1. + self.likelihood.precision*self.Diag0[:,None]) #NOTE: beta_star contains Diag0 and the precision
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self.V_star = self.beta_star * self.likelihood.Y
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# The rather complex computations of self.A
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if self.has_uncertain_inputs:
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raise NotImplementedError
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else:
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if self.likelihood.is_heteroscedastic:
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assert self.likelihood.output_dim == 1
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tmp = self.psi1 * (np.sqrt(self.beta_star.flatten().reshape(1, self.N)))
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tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
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self.A = tdot(tmp)
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tmp = self.psi1 * (np.sqrt(self.beta_star.flatten().reshape(1, self.N)))
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tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
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self.A = tdot(tmp)
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# factor B
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self.B = np.eye(self.M) + self.A
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self.B = np.eye(self.num_inducing) + self.A
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self.LB = jitchol(self.B)
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self.LBi = chol_inv(self.LB)
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self.psi1V = np.dot(self.psi1, self.V_star)
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@ -170,16 +115,10 @@ class FITC(SparseGP):
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for i,V_n,alpha_n,gamma_n,gamma_k in zip(range(self.N),self.V_star,alpha,gamma_2,gamma_3):
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K_pp_K = np.dot(Kmmipsi1[:,i:(i+1)],Kmmipsi1[:,i:(i+1)].T)
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#Diag_dpsi1 = Diag_dA_dpsi1: yT*beta_star*y + Diag_dC_dpsi1 +Diag_dD_dpsi1
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_dpsi1 = (-V_n**2 - alpha_n + 2.*gamma_k - gamma_n**2) * Kmmipsi1.T[i:(i+1),:]
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#Diag_dKmm = Diag_dA_dKmm: yT*beta_star*y +Diag_dC_dKmm +Diag_dD_dKmm
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_dKmm = .5*(V_n**2 + alpha_n + gamma_n**2 - 2.*gamma_k) * K_pp_K #Diag_dD_dKmm
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self._dpsi1_dtheta += self.kern.dK_dtheta(_dpsi1,self.X[i:i+1,:],self.Z)
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self._dKmm_dtheta += self.kern.dK_dtheta(_dKmm,self.Z)
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self._dKmm_dX += 2.*self.kern.dK_dX(_dKmm ,self.Z)
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self._dpsi1_dX += self.kern.dK_dX(_dpsi1.T,self.Z,self.X[i:i+1,:])
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@ -188,7 +127,7 @@ class FITC(SparseGP):
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# save computation here.
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self.partial_for_likelihood = None
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elif self.likelihood.is_heteroscedastic:
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raise NotImplementedError, "heteroscedatic derivates not implemented"
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raise NotImplementedError, "heteroscedatic derivates not implemented."
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else:
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# likelihood is not heterscedatic
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dbstar_dnoise = self.likelihood.precision * (self.beta_star**2 * self.Diag0[:,None] - self.beta_star)
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@ -225,35 +164,30 @@ class FITC(SparseGP):
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return np.hstack((self.dL_dZ().flatten(), self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood)))
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def dL_dtheta(self):
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if self.has_uncertain_inputs:
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raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
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else:
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dL_dtheta = self.kern.dKdiag_dtheta(self._dL_dpsi0,self.X)
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dL_dtheta += self.kern.dK_dtheta(self._dL_dpsi1,self.X,self.Z)
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dL_dtheta += self.kern.dK_dtheta(self._dL_dKmm,X=self.Z)
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dL_dtheta += self._dKmm_dtheta
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dL_dtheta += self._dpsi1_dtheta
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dL_dtheta = self.kern.dKdiag_dtheta(self._dL_dpsi0,self.X)
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dL_dtheta += self.kern.dK_dtheta(self._dL_dpsi1,self.X,self.Z)
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dL_dtheta += self.kern.dK_dtheta(self._dL_dKmm,X=self.Z)
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dL_dtheta += self._dKmm_dtheta
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dL_dtheta += self._dpsi1_dtheta
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return dL_dtheta
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def dL_dZ(self):
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if self.has_uncertain_inputs:
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raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
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else:
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dL_dZ = self.kern.dK_dX(self._dL_dpsi1.T,self.Z,self.X)
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dL_dZ += 2. * self.kern.dK_dX(self._dL_dKmm,X=self.Z)
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dL_dZ += self._dpsi1_dX
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dL_dZ += self._dKmm_dX
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dL_dZ = self.kern.dK_dX(self._dL_dpsi1.T,self.Z,self.X)
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dL_dZ += 2. * self.kern.dK_dX(self._dL_dKmm,X=self.Z)
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dL_dZ += self._dpsi1_dX
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dL_dZ += self._dKmm_dX
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return dL_dZ
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def _raw_predict(self, Xnew, which_parts, full_cov=False):
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def _raw_predict(self, Xnew, X_variance_new=None, which_parts='all', full_cov=False):
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assert X_variance_new is None, "FITC model is not defined for handling uncertain inputs."
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if self.likelihood.is_heteroscedastic:
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Iplus_Dprod_i = 1./(1.+ self.Diag0 * self.likelihood.precision.flatten())
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self.Diag = self.Diag0 * Iplus_Dprod_i
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self.P = Iplus_Dprod_i[:,None] * self.psi1.T
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self.RPT0 = np.dot(self.Lmi,self.psi1)
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self.L = np.linalg.cholesky(np.eye(self.M) + np.dot(self.RPT0,((1. - Iplus_Dprod_i)/self.Diag0)[:,None]*self.RPT0.T))
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self.R,info = linalg.flapack.dtrtrs(self.L,self.Lmi,lower=1)
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self.L = np.linalg.cholesky(np.eye(self.num_inducing) + np.dot(self.RPT0,((1. - Iplus_Dprod_i)/self.Diag0)[:,None]*self.RPT0.T))
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self.R,info = linalg.lapack.flapack.dtrtrs(self.L,self.Lmi,lower=1)
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self.RPT = np.dot(self.R,self.P.T)
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self.Sigma = np.diag(self.Diag) + np.dot(self.RPT.T,self.RPT)
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self.w = self.Diag * self.likelihood.v_tilde
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@ -275,8 +209,8 @@ class FITC(SparseGP):
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# = I - [RPT0] * (U*U.T)^-1 * [RPT0].T
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# = I - V.T * V
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U = np.linalg.cholesky(np.diag(self.Diag0) + self.Qnn)
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V,info = linalg.flapack.dtrtrs(U,self.RPT0.T,lower=1)
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C = np.eye(self.M) - np.dot(V.T,V)
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V,info = linalg.lapack.flapack.dtrtrs(U,self.RPT0.T,lower=1)
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C = np.eye(self.num_inducing) - np.dot(V.T,V)
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mu_u = np.dot(C,self.RPT0)*(1./self.Diag0[None,:])
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#self.C = C
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#self.RPT0 = np.dot(self.R0,self.Knm.T) P0.T
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@ -292,13 +226,13 @@ class FITC(SparseGP):
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mu_star = np.dot(KR0T,mu_H)
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if full_cov:
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Kxx = self.kern.K(Xnew,which_parts=which_parts)
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var = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T))
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var = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.num_inducing),KR0T.T))
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else:
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Kxx = self.kern.Kdiag(Xnew,which_parts=which_parts)
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var = (Kxx + np.sum(KR0T.T*np.dot(Sigma_H - np.eye(self.M),KR0T.T),0))[:,None]
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var = (Kxx + np.sum(KR0T.T*np.dot(Sigma_H - np.eye(self.num_inducing),KR0T.T),0))[:,None]
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return mu_star[:,None],var
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else:
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raise NotImplementedError, "homoscedastic FITC not implemented"
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raise NotImplementedError, "Heteroscedastic case not implemented."
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"""
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Kx = self.kern.K(self.Z, Xnew)
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mu = mdot(Kx.T, self.C/self.scale_factor, self.psi1V)
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