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made uncertain inputs a simple swith in the sparse GP class. This simplifies the inherritance structure
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James Hensman
parent
b1c2282bfc
commit
5f22bd00e6
2 changed files with 34 additions and 83 deletions
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@ -26,6 +26,8 @@ class sparse_GP_regression(GP_regression):
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:type kernel: a GPy kernel
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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 X_uncertainty: The uncertainty in the measurements of X (Gaussian variance)
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:type X_uncertainty: np.ndarray (N x Q) | None
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:param Zslices: slices for the inducing inputs (see slicing TODO: link)
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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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@ -44,6 +46,12 @@ class sparse_GP_regression(GP_regression):
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assert Z.shape[1]==X.shape[1]
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self.Z = Z
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self.M = Z.shape[1]
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if X_uncertainty is None:
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self.has_uncertain_inputs=False
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else:
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assert X_uncertainty.shape==X.shape
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self.has_uncertain_inputs=False
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self.X_uncertainty = X_uncertainty
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GP_regression.__init__(self, X, Y, kernel=kernel, normalize_X=normalize_X, normalize_Y=normalize_Y)
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self.trYYT = np.sum(np.square(self.Y))
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@ -58,13 +66,17 @@ class sparse_GP_regression(GP_regression):
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def _compute_kernel_matrices(self):
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# kernel computations, using BGPLVM notation
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#TODO: the following can be switched out in the case of uncertain inputs (or the BGPLVM!)
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#TODO: slices for psi statistics (easy enough)
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self.Kmm = self.kern.K(self.Z)
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self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices).sum()
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self.psi1 = self.kern.K(self.Z,self.X)
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self.psi2 = np.dot(self.psi1,self.psi1.T)
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if self.has_uncertain_inputs:
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self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
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self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
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self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)
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else:
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self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices).sum()
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self.psi1 = self.kern.K(self.Z,self.X)
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self.psi2 = np.dot(self.psi1,self.psi1.T)
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def _computations(self):
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# TODO find routine to multiply triangular matrices
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@ -132,12 +144,16 @@ class sparse_GP_regression(GP_regression):
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"""
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Compute and return the derivative of the log marginal likelihood wrt the parameters of the kernel
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"""
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#re-cast computations in psi2 back to psi1:
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dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
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dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm,self.Z)
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dL_dtheta += self.kern.dK_dtheta(dL_dpsi1,self.Z,self.X)
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dL_dtheta += self.kern.dKdiag_dtheta(self.dL_dpsi0, self.X)
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if self.has_uncertain_inputs:
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dL_dtheta += self.kern.dpsi0_dtheta(self.dL_dpsi0, self.Z,self.X,self.X_uncertainty)
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dL_dtheta += self.kern.dpsi1_dtheta(self.dL_dpsi1.T,self.Z,self.X, self.X_uncertainty)
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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
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else:
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#re-cast computations in psi2 back to psi1:
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dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
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dL_dtheta += self.kern.dK_dtheta(dL_dpsi1,self.Z,self.X)
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dL_dtheta += self.kern.dKdiag_dtheta(self.dL_dpsi0, self.X)
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return dL_dtheta
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@ -145,11 +161,14 @@ class sparse_GP_regression(GP_regression):
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"""
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The derivative of the bound wrt the inducing inputs Z
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"""
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#re-cast computations in psi2 back to psi1:
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dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
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dL_dZ = 2.*self.kern.dK_dX(self.dL_dKmm,self.Z,)#factor of two becase of vertical and horizontal 'stripes' in dKmm_dZ
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dL_dZ += self.kern.dK_dX(dL_dpsi1,self.Z,self.X)
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if self.has_uncertain_inputs:
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dL_dZ += self.kern.dpsi1_dZ(self.dL_dpsi1.T,self.Z,self.X, self.X_uncertainty)
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dL_dZ += self.kern.dpsi2_dZ(self.dL_dpsi2,self.Z,self.X, self.X_uncertainty)
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else:
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#re-cast computations in psi2 back to psi1:
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dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
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dL_dZ += self.kern.dK_dX(dL_dpsi1,self.Z,self.X)
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return dL_dZ
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def log_likelihood_gradients(self):
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@ -172,5 +191,7 @@ class sparse_GP_regression(GP_regression):
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GP_regression.plot(self,*args,**kwargs)
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if self.Q==1:
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pb.plot(self.Z,self.Z*0+pb.ylim()[0],'k|',mew=1.5,markersize=12)
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if self.has_uncertain_inputs:
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pb.errorbar(self.X[:,0], pb.ylim()[0]+np.zeros(self.N), xerr=2*np.sqrt(self.X_uncertainty.flatten()))
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if self.Q==2:
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pb.plot(self.Z[:,0],self.Z[:,1],'wo')
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@ -1,70 +0,0 @@
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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as np
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import pylab as pb
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from ..util.linalg import mdot, jitchol, chol_inv, pdinv
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from ..util.plot import gpplot
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from .. import kern
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from ..inference.likelihoods import likelihood
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from sparse_GP_regression import sparse_GP_regression
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class uncertain_input_GP_regression(sparse_GP_regression):
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"""
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Variational sparse GP model (Regression) with uncertainty on the inputs
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:param X: inputs
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:type X: np.ndarray (N x Q)
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:param X_uncertainty: uncertainty on X (Gaussian variances, assumed isotrpic)
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:type X_uncertainty: np.ndarray (N x Q)
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:param Y: observed data
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:type Y: np.ndarray of observations (N x D)
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:param kernel : the kernel/covariance function. See link kernels
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:type kernel: a GPy kernel
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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 Zslices: slices for the inducing inputs (see slicing TODO: link)
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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 beta: noise precision. TODO> ignore beta if doing EP
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:type beta: float
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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,Y,X_uncertainty,kernel=None, beta=100., Z=None,Zslices=None,M=10,normalize_X=False,normalize_Y=False):
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self.X_uncertainty = X_uncertainty
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sparse_GP_regression.__init__(self, X, Y, kernel = kernel, beta = beta, normalize_X = normalize_X, normalize_Y = normalize_Y)
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self.trYYT = np.sum(np.square(self.Y))
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def _compute_kernel_matrices(self):
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# kernel computations, using BGPLVM notation
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#TODO: slices for psi statistics (easy enough)
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self.Kmm = self.kern.K(self.Z)
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self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
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self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
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self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)
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def dL_dtheta(self):
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#re-cast computations in psi2 back to psi1:
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dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm,self.Z)
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dL_dtheta += self.kern.dpsi0_dtheta(self.dL_dpsi0, self.Z,self.X,self.X_uncertainty)
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dL_dtheta += self.kern.dpsi1_dtheta(self.dL_dpsi1.T,self.Z,self.X, self.X_uncertainty)
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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
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return dL_dtheta
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def dL_dZ(self):
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dL_dZ = 2.*self.kern.dK_dX(self.dL_dKmm,self.Z,)#factor of two becase of vertical and horizontal 'stripes' in dKmm_dZ
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dL_dZ += self.kern.dpsi1_dZ(self.dL_dpsi1.T,self.Z,self.X, self.X_uncertainty)
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dL_dZ += self.kern.dpsi2_dZ(self.dL_dpsi2,self.Z,self.X, self.X_uncertainty)
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return dL_dZ
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def plot(self,*args,**kwargs):
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"""
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Plot the fitted model: just call the sparse GP_regression plot function and then add
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markers to represent uncertainty on the inputs
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"""
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sparse_GP_regression.plot(self,*args,**kwargs)
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if self.Q==1:
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pb.errorbar(self.X[:,0], pb.ylim()[0]+np.zeros(self.N), xerr=2*np.sqrt(self.X_uncertainty.flatten()))
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