mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-05-15 06:52:39 +02:00
Merge changes for model.py and optimization.py on comments.
This commit is contained in:
Neil Lawrence
commit
60fd1c55dc
12 changed files with 336 additions and 195 deletions
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@ -10,6 +10,10 @@ from .. import kern
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from ..inference.likelihoods import likelihood
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from GP_regression import GP_regression
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#Still TODO:
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# make use of slices properly (kernel can now do this)
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# enable heteroscedatic noise (kernel will need to compute psi2 as a (NxMxM) array)
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class sparse_GP_regression(GP_regression):
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"""
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Variational sparse GP model (Regression)
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@ -22,6 +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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@ -31,7 +37,7 @@ class sparse_GP_regression(GP_regression):
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:type normalize_(X|Y): bool
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"""
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def __init__(self,X,Y,kernel=None, beta=100., Z=None,Zslices=None,M=10,normalize_X=False,normalize_Y=False):
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def __init__(self,X,Y,kernel=None, X_uncertainty=None, beta=100., Z=None,Zslices=None,M=10,normalize_X=False,normalize_Y=False):
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self.beta = beta
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if Z is None:
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self.Z = np.random.permutation(X.copy())[:M]
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@ -40,10 +46,20 @@ 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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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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#normalise X uncertainty also
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if self.has_uncertain_inputs:
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self.X_uncertainty /= np.square(self._Xstd)
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def set_param(self, p):
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self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
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self.beta = p[self.M*self.Q]
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@ -54,18 +70,23 @@ 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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self.psi1Y = np.dot(self.psi1, self.Y)
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self.psi1YYpsi1 = np.dot(self.psi1Y, self.psi1Y.T)
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self.V = self.beta*self.Y
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self.psi1V = np.dot(self.psi1, self.V)
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self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
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self.Lm = jitchol(self.Kmm)
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self.Lmi = chol_inv(self.Lm)
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self.Kmmi = np.dot(self.Lmi.T, self.Lmi)
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@ -77,25 +98,19 @@ class sparse_GP_regression(GP_regression):
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self.LLambdai = np.dot(self.LBi, self.Lmi)
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self.trace_K = self.psi0 - np.trace(self.A)
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self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
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self.C = mdot(self.LLambdai, self.psi1Y)
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self.G = mdot(self.LBL_inv, self.psi1YYpsi1, self.LBL_inv.T)
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self.C = mdot(self.LLambdai, self.psi1V)
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self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
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# Computes dL_dpsi
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# Compute dL_dpsi
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self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
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dC_dpsi1 = (self.LLambdai.T[:,:, None, None] * self.Y) # this is sane.
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tmp = (dC_dpsi1*self.C[None,:,None,:]).sum(1).sum(-1)
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self.dL_dpsi1 = self.beta2 * tmp
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self.dL_dpsi2 = (- 0.5 * self.D * self.beta * (self.LBL_inv - self.Kmmi)
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- self.beta**3 * 0.5 * self.G)
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dC_dpsi1 = (self.LLambdai.T[:,:, None, None] * self.V)
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self.dL_dpsi1 = (dC_dpsi1*self.C[None,:,None,:]).sum(1).sum(-1)
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self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
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# Computes dL_dKmm TODO: nicer precomputations
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tmp = self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi)
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self.dL_dKmm = -self.beta * self.D * 0.5 * mdot(self.Lmi.T, self.A, self.Lmi) # dB
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self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - tmp - tmp.T + self.Kmmi) # dC
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tmp = (mdot(self.LBL_inv, self.psi1YYpsi1, self.Kmmi)
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- self.beta*mdot(self.G, self.psi2, self.Kmmi))
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self.dL_dKmm += -0.5*self.beta2*(tmp + tmp.T - self.G) # dE
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# Compute dL_dKmm
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self.dL_dKmm = -0.5 * self.beta * self.D * mdot(self.Lmi.T, self.A, self.Lmi) # dB
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self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi) + self.Kmmi) # dC
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self.dL_dKmm += np.dot(np.dot(self.G,self.beta*self.psi2) - np.dot(self.LBL_inv, self.psi1VVpsi1), self.Kmmi) + 0.5*self.G # dE
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def get_param(self):
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return np.hstack([self.Z.flatten(),self.beta,self.kern.extract_param()])
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@ -104,65 +119,83 @@ class sparse_GP_regression(GP_regression):
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return sum([['iip_%i_%i'%(i,j) for i in range(self.Z.shape[0])] for j in range(self.Z.shape[1])],[]) + ['noise_precision']+self.kern.extract_param_names()
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def log_likelihood(self):
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"""
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Compute the (lower bound on the) log marginal likelihood
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"""
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A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta))
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B = -0.5*self.beta*self.D*self.trace_K
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C = -self.D * np.sum(np.log(np.diag(self.LB)))
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D = -0.5*self.beta*self.trYYT
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E = +0.5*self.beta2*np.sum(self.psi1YYpsi1 * self.LBL_inv)
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E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
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return A+B+C+D+E
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def dL_dbeta(self):
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""" compute the gradient of the log likelihood wrt beta.
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TODO: suport heteroscedatic noise"""
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"""
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Compute the gradient of the log likelihood wrt beta.
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TODO: suport heteroscedatic noise
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"""
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dA_dbeta = 0.5 * self.N*self.D/self.beta
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dB_dbeta = - 0.5 * self.D * self.trace_K
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dC_dbeta = - 0.5 * self.D * np.sum(self.Bi*self.A)
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dD_dbeta = - 0.5 * self.trYYT
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tmp = mdot(self.LBi.T, self.LLambdai, self.psi1Y)
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dE_dbeta = (self.beta * np.sum(np.square(self.C)) - 0.5 * self.beta2
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* np.sum(self.A * np.dot(tmp, tmp.T)))
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tmp = mdot(self.LBi.T, self.LLambdai, self.psi1V)
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dE_dbeta = np.sum(np.square(self.C))/self.beta - 0.5 * np.sum(self.A * np.dot(tmp, tmp.T))
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return np.squeeze(dA_dbeta + dB_dbeta + dC_dbeta + dD_dbeta + dE_dbeta)
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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_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
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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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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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def dL_dZ(self):
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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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"""
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The derivative of the bound wrt the inducing inputs Z
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"""
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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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return np.hstack([self.dL_dZ().flatten(), self.dL_dbeta(), self.dL_dtheta()])
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def _raw_predict(self,Xnew,slices):
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def _raw_predict(self, Xnew, slices):
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"""Internal helper function for making predictions, does not account for normalisation"""
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Kx = self.kern.K(self.Z, Xnew)
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Kxx = self.kern.K(Xnew)
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mu = self.beta * mdot(Kx.T, self.LBL_inv, self.psi1Y)
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mu = mdot(Kx.T, self.LBL_inv, self.psi1V)
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var = Kxx - mdot(Kx.T, (self.Kmmi - self.LBL_inv), Kx) + np.eye(Xnew.shape[0])/self.beta # TODO: This beta doesn't belong here in the EP case.
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return mu,var
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def plot(self,*args,**kwargs):
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def plot(self, *args, **kwargs):
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"""
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Plot the fitted model: just call the GP_regression plot function and then add inducing inputs
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"""
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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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128
GPy/models/uncollapsed_sparse_GP.py
Normal file
128
GPy/models/uncollapsed_sparse_GP.py
Normal file
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@ -0,0 +1,128 @@
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# Copyright (c) 2012 James Hensman
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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 uncollapsed_sparse_GP(sparse_GP_regression):
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"""
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Variational sparse GP model (Regression), where the approximating distribution q(u) is represented explicitly
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:param X: inputs
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:type X: 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 q_u: canonical parameters of the distribution squasehd into a 1D array
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:type q_u: np.ndarray
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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
|
||||
:param beta: noise precision. TODO> ignore beta if doing EP
|
||||
:type beta: float
|
||||
:param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
|
||||
:type normalize_(X|Y): bool
|
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"""
|
||||
|
||||
def __init__(self, X, Y, q_u=None, *args, **kwargs)
|
||||
D = Y.shape[1]
|
||||
if q_u is None:
|
||||
if Z is None:
|
||||
M = Z.shape[0]
|
||||
else:
|
||||
M=M
|
||||
self.set_vb_param(np.hstack((np.ones(M*D)),np.eye(M).flatten()))
|
||||
sparse_GP_regression.__init__(self, X, Y, *args, **kwargs)
|
||||
|
||||
def _computations(self):
|
||||
self.V = self.beta*self.Y
|
||||
self.psi1V = np.dot(self.psi1, self.V)
|
||||
self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
|
||||
self.Lm = jitchol(self.Kmm)
|
||||
self.Lmi = chol_inv(self.Lm)
|
||||
self.Kmmi = np.dot(self.Lmi.T, self.Lmi)
|
||||
self.A = mdot(self.Lmi, self.psi2, self.Lmi.T)
|
||||
self.B = np.eye(self.M) + self.beta * self.A
|
||||
self.Lambda = mdot(self.Lmi.T,self.B,sel.Lmi)
|
||||
|
||||
# Compute dL_dpsi
|
||||
self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
|
||||
self.dL_dpsi1 =
|
||||
self.dL_dpsi2 =
|
||||
|
||||
# Compute dL_dKmm
|
||||
self.dL_dKmm =
|
||||
self.dL_dKmm +=
|
||||
self.dL_dKmm +=
|
||||
|
||||
def log_likelihood(self):
|
||||
"""
|
||||
Compute the (lower bound on the) log marginal likelihood
|
||||
"""
|
||||
A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta))
|
||||
B = -0.5*self.beta*self.D*self.trace_K
|
||||
C = -self.D *(self.Kmm_hld +0.5*np.sum(self.Lambda * self.mmT_S) + self.M/2.)
|
||||
E = -0.5*self.beta*self.trYYT
|
||||
F = np.sum(np.dot(self.V.T,self.projected_mean))
|
||||
return A+B+C+D+E+F
|
||||
|
||||
def dL_dbeta(self):
|
||||
"""
|
||||
Compute the gradient of the log likelihood wrt beta.
|
||||
TODO: suport heteroscedatic noise
|
||||
"""
|
||||
dA_dbeta = 0.5 * self.N*self.D/self.beta
|
||||
dB_dbeta = - 0.5 * self.D * self.trace_K
|
||||
dC_dbeta = - 0.5 * self.D * #TODO
|
||||
dD_dbeta = - 0.5 * self.trYYT
|
||||
|
||||
return np.squeeze(dA_dbeta + dB_dbeta + dC_dbeta + dD_dbeta + dE_dbeta)
|
||||
|
||||
def _raw_predict(self, Xnew, slices):
|
||||
"""Internal helper function for making predictions, does not account for normalisation"""
|
||||
|
||||
#TODO
|
||||
return mu,var
|
||||
|
||||
def set_vb_param(self,vb_param):
|
||||
"""set the distribution q(u) from the canonical parameters"""
|
||||
self.q_u_prec = -2.*vb_param[self.M*self.D:].reshape(self.M,self.M)
|
||||
self.q_u_prec_L = jitchol(self.q_u_prec)
|
||||
self.q_u_cov_L = chol_inv(self.q_u_prec_L)
|
||||
self.q_u_cov = np.dot(self.q_u_cov_L,self.q_u_cov_L.T)
|
||||
self.q_u_mean = -2.*np.dot(self.q_u_cov,vb_param[:self.M*self.D].reshape(self.M,self.D))
|
||||
|
||||
self.q_u_expectation = (self.q_u_mean, np.dot(self.q_u_mean,self.q_u_mean.T)+self.q_u_cov)
|
||||
|
||||
self.q_u_canonical = (np.dot(self.q_u_prec, self.q_u_mean),-0.5*self.q_u_prec)
|
||||
#TODO: computations now?
|
||||
|
||||
def get_vb_param(self):
|
||||
"""
|
||||
Return the canonical parameters of the distribution q(u)
|
||||
"""
|
||||
return np.hstack([e.flatten() for e in self.q_u_canonical])
|
||||
|
||||
def vb_grad_natgrad(self):
|
||||
"""
|
||||
Compute the gradients of the lower bound wrt the canonical and
|
||||
Expectation parameters of u.
|
||||
|
||||
Note that the natural gradient in either is given by the gradient in the other (See Hensman et al 2012 Fast Variational inference in the conjugate exponential Family)
|
||||
"""
|
||||
foobar #TODO
|
||||
|
||||
def plot(self, *args, **kwargs):
|
||||
"""
|
||||
add the distribution q(u) to the plot from sparse_GP_regression
|
||||
"""
|
||||
sparse_GP_regression.plot(self,*args,**kwargs)
|
||||
#TODO: plot the q(u) dist.
|
||||
Loading…
Add table
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Reference in a new issue