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[sparse gp] prediction with uncertain inputs

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mzwiessele 2015-02-21 14:43:10 +01:00
parent 9f7ae611ed
commit 6435b83c7a
2 changed files with 42 additions and 51 deletions
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52
GPy/core/sparse_gp.py
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@ -6,7 +6,8 @@ from gp import GP
from parameterization.param import Param
from ..inference.latent_function_inference import var_dtc
from .. import likelihoods
from parameterization.variational import VariationalPosterior
from parameterization.variational import VariationalPosterior, NormalPosterior
from ..util.linalg import mdot
import logging
from GPy.inference.latent_function_inference.posterior import Posterior
@ -102,7 +103,15 @@ class SparseGP(GP):
def _raw_predict(self, Xnew, full_cov=False, kern=None):
"""
Make a prediction for the latent function values
Make a prediction for the latent function values.
For certain inputs we give back a full_cov of shape NxN,
if there is missing data, each dimension has its own full_cov of shape NxNxD, and if full_cov is of,
we take only the diagonal elements across N.
For uncertain inputs, the SparseGP bound produces a full covariance structure across D, so for full_cov we
return a NxDxD matrix and in the not full_cov case, we return the diagonal elements across D (NxD).
This is for both with and without missing data.
"""
if kern is None: kern = self.kern
@ -121,15 +130,32 @@ class SparseGP(GP):
Kxx = kern.Kdiag(Xnew)
var = (Kxx - np.sum(np.dot(np.atleast_3d(self.posterior.woodbury_inv).T, Kx) * Kx[None,:,:], 1)).T
else:
Kx = kern.psi1(self.Z, Xnew).T
mu = np.dot(Kx.T, self.posterior.woodbury_vector)
if full_cov:
Kxx = kern.K(Xnew.mean)
if self.posterior.woodbury_inv.ndim == 2:
var = Kxx - np.dot(Kx.T, np.dot(self.posterior.woodbury_inv, Kx))
elif self.posterior.woodbury_inv.ndim == 3:
var = Kxx[:,:,None] - np.tensordot(np.dot(np.atleast_3d(self.posterior.woodbury_inv).T, Kx).T, Kx, [1,0]).swapaxes(1,2)
else:
Kxx = kern.psi0(self.Z, Xnew)
var = (Kxx - np.sum(np.dot(np.atleast_3d(self.posterior.woodbury_inv).T, Kx) * Kx[None,:,:], 1)).T
psi0_star = self.kern.psi0(self.Z, Xnew)
psi1_star = self.kern.psi1(self.Z, Xnew)
#psi2_star = self.kern.psi2(self.Z, Xnew) # Only possible if we get NxMxM psi2 out of the code.
la = self.posterior.woodbury_vector
mu = np.dot(psi1_star, la) # TODO: dimensions?
if full_cov:
var = np.empty((Xnew.shape[0], la.shape[1], la.shape[1]))
di = np.diag_indices(la.shape[1])
else:
var = np.empty((Xnew.shape[0], la.shape[1]))
for i in range(Xnew.shape[0]):
_mu, _var = Xnew.mean.values[[i]], Xnew.variance.values[[i]]
psi2_star = self.kern.psi2(self.Z, NormalPosterior(_mu, _var))
tmp = (psi2_star[:, :] - psi1_star[[i]].T.dot(psi1_star[[i]]))
var_ = mdot(la.T, tmp, la)
p0 = psi0_star[i]
t = self.posterior.woodbury_inv
t2 = np.trace(t.T.dot(psi2_star), axis1=1, axis2=2)
if full_cov:
var_[di] += p0
var_[di] += -t2
var[i] = var_
else:
var[i] = np.diag(var_)+p0-t2
return mu, var