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Merge pull request #599 from marpulli/grads_efficiency

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Make predictive_gradients more efficient
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Zhenwen Dai 2018-02-09 07:22:56 +00:00 • committed by GitHub
commit 4f739b1589
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1 changed files with 26 additions and 16 deletions
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GPy/core/gp.py
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@ -376,13 +376,16 @@ class GP(Model):
def predictive_gradients(self, Xnew, kern=None):
"""
Compute the derivatives of the predicted latent function with respect to X*
Compute the derivatives of the predicted latent function with respect
to X*
Given a set of points at which to predict X* (size [N*,Q]), compute the
derivatives of the mean and variance. Resulting arrays are sized:
dmu_dX* -- [N*, Q ,D], where D is the number of output in this GP (usually one).
dmu_dX* -- [N*, Q ,D], where D is the number of output in this GP
(usually one).
Note that this is not the same as computing the mean and variance of the derivative of the function!
Note that this is not the same as computing the mean and variance of
the derivative of the function!
dv_dX* -- [N*, Q], (since all outputs have the same variance)
:param X: The points at which to get the predictive gradients
@ -393,25 +396,32 @@ class GP(Model):
"""
if kern is None:
kern = self.kern
mean_jac = np.empty((Xnew.shape[0],Xnew.shape[1],self.output_dim))
mean_jac = np.empty((Xnew.shape[0], Xnew.shape[1], self.output_dim))
for i in range(self.output_dim):
mean_jac[:,:,i] = kern.gradients_X(self.posterior.woodbury_vector[:,i:i+1].T, Xnew, self._predictive_variable)
mean_jac[:, :, i] = kern.gradients_X(
self.posterior.woodbury_vector[:, i:i+1].T, Xnew,
self._predictive_variable)
# gradients wrt the diagonal part k_{xx}
dv_dX = kern.gradients_X(np.eye(Xnew.shape[0]), Xnew)
#grads wrt 'Schur' part K_{xf}K_{ff}^{-1}K_{fx}
# Gradients wrt the diagonal part k_{xx}
dv_dX = kern.gradients_X_diag(np.ones(Xnew.shape[0]), Xnew)
# Grads wrt 'Schur' part K_{xf}K_{ff}^{-1}K_{fx}
if self.posterior.woodbury_inv.ndim == 3:
tmp = np.empty(dv_dX.shape + (self.posterior.woodbury_inv.shape[2],))
tmp[:] = dv_dX[:,:,None]
var_jac = np.empty(dv_dX.shape +
(self.posterior.woodbury_inv.shape[2],))
var_jac[:] = dv_dX[:, :, None]
for i in range(self.posterior.woodbury_inv.shape[2]):
alpha = -2.*np.dot(kern.K(Xnew, self._predictive_variable), self.posterior.woodbury_inv[:, :, i])
tmp[:, :, i] += kern.gradients_X(alpha, Xnew, self._predictive_variable)
alpha = -2.*np.dot(kern.K(Xnew, self._predictive_variable),
self.posterior.woodbury_inv[:, :, i])
var_jac[:, :, i] += kern.gradients_X(alpha, Xnew,
self._predictive_variable)
else:
tmp = dv_dX
alpha = -2.*np.dot(kern.K(Xnew, self._predictive_variable), self.posterior.woodbury_inv)
tmp += kern.gradients_X(alpha, Xnew, self._predictive_variable)
return mean_jac, tmp
var_jac = dv_dX
alpha = -2.*np.dot(kern.K(Xnew, self._predictive_variable),
self.posterior.woodbury_inv)
var_jac += kern.gradients_X(alpha, Xnew, self._predictive_variable)
return mean_jac, var_jac
def predict_jacobian(self, Xnew, kern=None, full_cov=False):
"""