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move _raw_predict into posterior object
This commit is contained in:
Zhenwen Dai
parent
f2b813551a
commit
67ba9b60c6
4 changed files with 53 additions and 121 deletions
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@ -212,42 +212,9 @@ class GP(Model):
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= N(f*| K_{x*x}(K_{xx} + \Sigma)^{-1}Y, K_{x*x*} - K_{xx*}(K_{xx} + \Sigma)^{-1}K_{xx*}
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\Sigma := \texttt{Likelihood.variance / Approximate likelihood covariance}
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"""
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if hasattr(self.posterior, '_raw_predict'):
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mu, var = self.posterior._raw_predict(kern=self.kern if kern is None else kern, Xnew=Xnew, pred_var=self._predictive_variable, full_cov=full_cov)
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if self.mean_function is not None:
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mu += self.mean_function.f(Xnew)
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return mu, var
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if kern is None:
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kern = self.kern
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Kx = kern.K(self._predictive_variable, Xnew)
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mu = np.dot(Kx.T, self.posterior.woodbury_vector)
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if len(mu.shape)==1:
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mu = mu.reshape(-1,1)
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if full_cov:
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Kxx = kern.K(Xnew)
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if self.posterior.woodbury_inv.ndim == 2:
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var = Kxx - np.dot(Kx.T, np.dot(self.posterior.woodbury_inv, Kx))
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elif self.posterior.woodbury_inv.ndim == 3: # Missing data
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var = np.empty((Kxx.shape[0],Kxx.shape[1],self.posterior.woodbury_inv.shape[2]))
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from ..util.linalg import mdot
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for i in range(var.shape[2]):
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var[:, :, i] = (Kxx - mdot(Kx.T, self.posterior.woodbury_inv[:, :, i], Kx))
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var = var
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else:
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Kxx = kern.Kdiag(Xnew)
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if self.posterior.woodbury_inv.ndim == 2:
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var = (Kxx - np.sum(np.dot(self.posterior.woodbury_inv.T, Kx) * Kx, 0))[:,None]
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elif self.posterior.woodbury_inv.ndim == 3: # Missing data
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var = np.empty((Kxx.shape[0],self.posterior.woodbury_inv.shape[2]))
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for i in range(var.shape[1]):
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var[:, i] = (Kxx - (np.sum(np.dot(self.posterior.woodbury_inv[:, :, i].T, Kx) * Kx, 0)))
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var = var
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#add in the mean function
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mu, var = self.posterior._raw_predict(kern=self.kern if kern is None else kern, Xnew=Xnew, pred_var=self._predictive_variable, full_cov=full_cov)
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if self.mean_function is not None:
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mu += self.mean_function.f(Xnew)
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return mu, var
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def predict(self, Xnew, full_cov=False, Y_metadata=None, kern=None, likelihood=None):
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@ -113,90 +113,3 @@ class SparseGP(GP):
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self.Z.gradient += self.kern.gradients_X(self.grad_dict['dL_dKnm'].T, self.Z, self.X)
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self._Zgrad = self.Z.gradient.copy()
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def _raw_predict(self, Xnew, full_cov=False, kern=None):
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"""
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Make a prediction for the latent function values.
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For certain inputs we give back a full_cov of shape NxN,
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if there is missing data, each dimension has its own full_cov of shape NxNxD, and if full_cov is of,
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we take only the diagonal elements across N.
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For uncertain inputs, the SparseGP bound produces cannot predict the full covariance matrix full_cov for now.
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The implementation of that will follow. However, for each dimension the
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covariance changes, so if full_cov is False (standard), we return the variance
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for each dimension [NxD].
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"""
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if hasattr(self.posterior, '_raw_predict'):
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mu, var = self.posterior._raw_predict(kern=self.kern if kern is None else kern, Xnew=Xnew, pred_var=self._predictive_variable, full_cov=full_cov)
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if self.mean_function is not None:
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mu += self.mean_function.f(Xnew)
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return mu, var
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if kern is None: kern = self.kern
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if not isinstance(Xnew, VariationalPosterior):
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# Kx = kern.K(self._predictive_variable, Xnew)
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# mu = np.dot(Kx.T, self.posterior.woodbury_vector)
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# if full_cov:
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# Kxx = kern.K(Xnew)
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# if self.posterior.woodbury_inv.ndim == 2:
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# var = Kxx - np.dot(Kx.T, np.dot(self.posterior.woodbury_inv, Kx))
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# elif self.posterior.woodbury_inv.ndim == 3:
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# var = np.empty((Kxx.shape[0],Kxx.shape[1],self.posterior.woodbury_inv.shape[2]))
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# for i in range(var.shape[2]):
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# var[:, :, i] = (Kxx - mdot(Kx.T, self.posterior.woodbury_inv[:, :, i], Kx))
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# var = var
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# else:
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# Kxx = kern.Kdiag(Xnew)
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# if self.posterior.woodbury_inv.ndim == 2:
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# var = (Kxx - np.sum(np.dot(self.posterior.woodbury_inv.T, Kx) * Kx, 0))[:,None]
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# elif self.posterior.woodbury_inv.ndim == 3:
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# var = np.empty((Kxx.shape[0],self.posterior.woodbury_inv.shape[2]))
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# for i in range(var.shape[1]):
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# var[:, i] = (Kxx - (np.sum(np.dot(self.posterior.woodbury_inv[:, :, i].T, Kx) * Kx, 0)))
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# var = var
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# #add in the mean function
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# if self.mean_function is not None:
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# mu += self.mean_function.f(Xnew)
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mu, var = super(SparseGP, self)._raw_predict(Xnew, full_cov, kern)
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else:
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psi0_star = kern.psi0(self._predictive_variable, Xnew)
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psi1_star = kern.psi1(self._predictive_variable, Xnew)
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psi2_star = kern.psi2n(self._predictive_variable, Xnew)
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la = self.posterior.woodbury_vector
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mu = np.dot(psi1_star, la) # TODO: dimensions?
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N,M,D = psi0_star.shape[0],psi1_star.shape[1], la.shape[1]
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if full_cov:
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raise NotImplementedError("Full covariance for Sparse GP predicted with uncertain inputs not implemented yet.")
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var = np.zeros((Xnew.shape[0], la.shape[1], la.shape[1]))
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di = np.diag_indices(la.shape[1])
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else:
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tmp = psi2_star - psi1_star[:,:,None]*psi1_star[:,None,:]
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var = (tmp.reshape(-1,M).dot(la).reshape(N,M,D)*la[None,:,:]).sum(1) + psi0_star[:,None]
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if self.posterior.woodbury_inv.ndim==2:
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var += -psi2_star.reshape(N,-1).dot(self.posterior.woodbury_inv.flat)[:,None]
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else:
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var += -psi2_star.reshape(N,-1).dot(self.posterior.woodbury_inv.reshape(-1,D))
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assert np.all(var>=-1e-5), "The predicted variance goes negative!: "+str(var)
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var = np.clip(var,1e-15,np.inf)
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# for i in range(Xnew.shape[0]):
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# _mu, _var = Xnew.mean.values[[i]], Xnew.variance.values[[i]]
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# psi2_star = kern.psi2(self._predictive_variable, NormalPosterior(_mu, _var))
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# tmp = (psi2_star[:, :] - psi1_star[[i]].T.dot(psi1_star[[i]]))
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#
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# var_ = mdot(la.T, tmp, la)
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# p0 = psi0_star[i]
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# t = np.atleast_3d(self.posterior.woodbury_inv)
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# t2 = np.trace(t.T.dot(psi2_star), axis1=1, axis2=2)
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#
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# if full_cov:
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# var_[di] += p0
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# var_[di] += -t2
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# var[i] = var_
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# else:
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# var[i] = np.diag(var_)+p0-t2
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return mu, var
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@ -3,6 +3,7 @@
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import numpy as np
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from ...util.linalg import pdinv, dpotrs, dpotri, symmetrify, jitchol, dtrtrs, tdot
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from GPy.core.parameterization.variational import VariationalPosterior
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class Posterior(object):
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"""
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@ -187,6 +188,56 @@ class Posterior(object):
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if self._K_chol is None:
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self._K_chol = jitchol(self._K)
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return self._K_chol
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def _raw_predict(self, kern, Xnew, pred_var, full_cov=False):
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woodbury_vector = self.woodbury_vector
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woodbury_inv = self.woodbury_inv
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if not isinstance(Xnew, VariationalPosterior):
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Kx = kern.K(pred_var, Xnew)
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mu = np.dot(Kx.T, woodbury_vector)
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if len(mu.shape)==1:
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mu = mu.reshape(-1,1)
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if full_cov:
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Kxx = kern.K(Xnew)
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if woodbury_inv.ndim == 2:
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var = Kxx - np.dot(Kx.T, np.dot(woodbury_inv, Kx))
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elif woodbury_inv.ndim == 3: # Missing data
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var = np.empty((Kxx.shape[0],Kxx.shape[1],woodbury_inv.shape[2]))
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from ...util.linalg import mdot
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for i in range(var.shape[2]):
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var[:, :, i] = (Kxx - mdot(Kx.T, woodbury_inv[:, :, i], Kx))
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var = var
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else:
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Kxx = kern.Kdiag(Xnew)
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if woodbury_inv.ndim == 2:
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var = (Kxx - np.sum(np.dot(woodbury_inv.T, Kx) * Kx, 0))[:,None]
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elif woodbury_inv.ndim == 3: # Missing data
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var = np.empty((Kxx.shape[0],woodbury_inv.shape[2]))
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for i in range(var.shape[1]):
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var[:, i] = (Kxx - (np.sum(np.dot(woodbury_inv[:, :, i].T, Kx) * Kx, 0)))
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var = var
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else:
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psi0_star = kern.psi0(pred_var, Xnew)
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psi1_star = kern.psi1(pred_var, Xnew)
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psi2_star = kern.psi2n(pred_var, Xnew)
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la = woodbury_vector
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mu = np.dot(psi1_star, la) # TODO: dimensions?
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N,M,D = psi0_star.shape[0],psi1_star.shape[1], la.shape[1]
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if full_cov:
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raise NotImplementedError("Full covariance for Sparse GP predicted with uncertain inputs not implemented yet.")
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var = np.zeros((Xnew.shape[0], la.shape[1], la.shape[1]))
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di = np.diag_indices(la.shape[1])
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else:
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tmp = psi2_star - psi1_star[:,:,None]*psi1_star[:,None,:]
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var = (tmp.reshape(-1,M).dot(la).reshape(N,M,D)*la[None,:,:]).sum(1) + psi0_star[:,None]
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if woodbury_inv.ndim==2:
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var += -psi2_star.reshape(N,-1).dot(woodbury_inv.flat)[:,None]
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else:
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var += -psi2_star.reshape(N,-1).dot(woodbury_inv.reshape(-1,D))
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var = np.clip(var,1e-15,np.inf)
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return mu, var
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class PosteriorExact(Posterior):
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@ -157,6 +157,7 @@ class MiscTests(unittest.TestCase):
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# Not easy to check if woodbury_inv is correct in itself as it requires a large derivation and expression
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Kinv = m.posterior.woodbury_inv
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K_hat = k.K(self.X_new) - k.K(self.X_new, Z).dot(Kinv).dot(k.K(Z, self.X_new))
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K_hat = np.clip(K_hat, 1e-15, np.inf)
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mu, covar = m._raw_predict(self.X_new, full_cov=True)
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self.assertEquals(mu.shape, (self.N_new, self.D))
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