mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-05-09 12:02:38 +02:00
Other changes.
This commit is contained in:
Ricardo Andrade
parent
fad0e07624
commit
29ec128c9d
7 changed files with 164 additions and 143 deletions
|
|
@ -37,7 +37,7 @@ class sparse_GP(GP):
|
|||
:type normalize_(X|Y): bool
|
||||
"""
|
||||
|
||||
def __init__(self,X,Y,kernel=None, X_uncertainty=None, beta=100., Z=None,Zslices=None,M=10,normalize_X=False,normalize_Y=False,likelihood=None,method_ep='DTC',epsilon_ep=1e-3,epsilon_em=.1,power_ep=[1.,1.]):
|
||||
def __init__(self,X,Y=None,kernel=None, X_uncertainty=None, beta=100., Z=None,Zslices=None,M=10,normalize_X=False,normalize_Y=False,likelihood=None,method_ep='DTC',epsilon_ep=1e-3,epsilon_em=.1,power_ep=[1.,1.]):
|
||||
|
||||
if Z is None:
|
||||
self.Z = np.random.permutation(X.copy())[:M]
|
||||
|
|
@ -53,10 +53,8 @@ class sparse_GP(GP):
|
|||
self.has_uncertain_inputs=True
|
||||
self.X_uncertainty = X_uncertainty
|
||||
|
||||
|
||||
self.beta = beta #FIXME
|
||||
GP.__init__(self, X, Y, kernel=kernel, normalize_X=normalize_X, normalize_Y=normalize_Y,likelihood=likelihood,epsilon_ep=epsilon_ep,epsion_em=epsilon_em,power_ep=power_ep)
|
||||
self.beta = beta if isinstance(likelihood,gaussian) else self.tau_tilde #TODO this should be defined in GP.__init__
|
||||
GP.__init__(self, X=X, Y=Y, kernel=kernel, normalize_X=normalize_X, normalize_Y=normalize_Y,likelihood=likelihood,epsilon_ep=epsilon_ep,epsilon_em=epsilon_em,power_ep=power_ep)
|
||||
self.trYYT = np.sum(np.square(self.Y)) if not self.EP else None
|
||||
|
||||
|
||||
#normalise X uncertainty also
|
||||
|
|
@ -74,10 +72,55 @@ class sparse_GP(GP):
|
|||
else:
|
||||
self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
|
||||
self.kern._set_params(p[self.Z.size:])
|
||||
#self._compute_kernel_matrices() this is replaced by _ep_covariance
|
||||
self._ep_covariance()
|
||||
#self._compute_kernel_matrices() this is replaced by _ep_kernel_matrices
|
||||
self._ep_kernel_matrices()
|
||||
self._ep_computations()
|
||||
|
||||
def _compute_kernel_matrices(self):
|
||||
# kernel computations, using BGPLVM notation
|
||||
#TODO: slices for psi statistics (easy enough)
|
||||
|
||||
self.Kmm = self.kern.K(self.Z)
|
||||
if self.has_uncertain_inputs:
|
||||
if self.hetero_noise:
|
||||
raise NotImplementedError, "uncertain ips and het noise not yet supported"
|
||||
else:
|
||||
self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
|
||||
self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
|
||||
self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)
|
||||
else:
|
||||
if self.hetero_noise:
|
||||
print "rick's stuff here"
|
||||
else:
|
||||
self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices).sum()
|
||||
self.psi1 = self.kern.K(self.Z,self.X)
|
||||
self.psi2 = np.dot(self.psi1,self.psi1.T)
|
||||
|
||||
def _computations(self):
|
||||
# TODO find routine to multiply triangular matrices
|
||||
self.V = self.beta*self.Y
|
||||
self.psi1V = np.dot(self.psi1, self.V)
|
||||
self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
|
||||
self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
|
||||
self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T)
|
||||
self.B = np.eye(self.M) + self.A
|
||||
self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
|
||||
self.LLambdai = np.dot(self.LBi, self.Lmi)
|
||||
self.trace_K = self.psi0 - np.trace(self.A)/self.beta
|
||||
self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
|
||||
self.C = mdot(self.LLambdai, self.psi1V)
|
||||
self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
|
||||
|
||||
# Compute dL_dpsi
|
||||
self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
|
||||
self.dL_dpsi1 = mdot(self.LLambdai.T,self.C,self.V.T)
|
||||
self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
|
||||
|
||||
# Compute dL_dKmm
|
||||
self.dL_dKmm = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi) # dB
|
||||
self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi) + self.Kmmi) # dC
|
||||
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
|
||||
|
||||
def approximate_likelihood(self):
|
||||
assert not isinstance(self.likelihood, gaussian), "EP is only available for non-gaussian likelihoods"
|
||||
if self.ep_proxy == 'DTC':
|
||||
|
|
@ -88,6 +131,22 @@ class sparse_GP(GP):
|
|||
else:
|
||||
self.ep_approx = Full(self.X,self.likelihood,self.kernel,inducing=None,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
|
||||
self.beta, self.v_tilde, self.Z_hat, self.tau_, self.v_=self.ep_approx.fit_EP()
|
||||
self._ep_kernel_matrices()
|
||||
self._computations()
|
||||
|
||||
def _ep_kernel_matrices(self):
|
||||
self.Kmm = self.kern.K(self.Z)
|
||||
if self.has_uncertain_inputs:
|
||||
self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
|
||||
self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
|
||||
self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty) #FIXME include beta
|
||||
else:
|
||||
self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices)
|
||||
self.psi1 = self.kern.K(self.Z,self.X)
|
||||
self.psi2 = np.dot(self.psi1,self.psi1.T)
|
||||
self.psi2_beta_scaled = np.dot(self.psi1,self.beta*self.psi1.T)
|
||||
|
||||
def _ep_computations(self):
|
||||
# Y: EP likelihood is defined as a regression model for mu_tilde
|
||||
self.Y = self.v_tilde/self.beta
|
||||
self._Ymean = np.zeros((1,self.Y.shape[1]))
|
||||
|
|
@ -99,50 +158,17 @@ class sparse_GP(GP):
|
|||
else:
|
||||
self.YYT = None
|
||||
self.mu_ = self.v_/self.tau_
|
||||
self._ep_covariance()
|
||||
self._computations()
|
||||
|
||||
def _ep_covariance(self):
|
||||
self.Kmm = self.kern.K(self.Z)
|
||||
if self.has_uncertain_inputs:
|
||||
self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
|
||||
self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
|
||||
self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty) #FIXME include beta
|
||||
else:
|
||||
#self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices).sum()
|
||||
self.Knn_diag = self.kern.Kdiag(self.X,slices=self.Xslices)
|
||||
self.psi0 = (self.beta*self.Knn_diag).sum() #TODO check dimensions
|
||||
self.psi1 = self.kern.K(self.Z,self.X)
|
||||
#self.psi2 = np.dot(self.psi1,self.psi1.T)
|
||||
self.psi2 = np.dot(self.psi1,self.beta*self.psi1.T)
|
||||
|
||||
def _compute_kernel_matrices(self):
|
||||
# kernel computations, using BGPLVM notation
|
||||
#TODO: slices for psi statistics (easy enough)
|
||||
|
||||
self.Kmm = self.kern.K(self.Z)
|
||||
if self.has_uncertain_inputs:
|
||||
self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
|
||||
self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
|
||||
self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)
|
||||
else:
|
||||
self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices).sum()
|
||||
self.psi1 = self.kern.K(self.Z,self.X)
|
||||
self.psi2 = np.dot(self.psi1,self.psi1.T)
|
||||
|
||||
def _ep_computations(self):
|
||||
# TODO find routine to multiply triangular matrices
|
||||
self.V = self.beta*self.Y
|
||||
self.psi1V = np.dot(self.psi1, self.V)
|
||||
self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
|
||||
self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
|
||||
#self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T)
|
||||
self.A = mdot(self.Lmi, self.psi2, self.Lmi.T)
|
||||
self.A = mdot(self.Lmi, self.psi2_beta_scaled, self.Lmi.T)
|
||||
self.B = np.eye(self.M) + self.A
|
||||
self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
|
||||
self.LLambdai = np.dot(self.LBi, self.Lmi)
|
||||
#self.trace_K = self.psi0 - np.sum(np.dot(self.Lmi,self.psi1)**2,-1) #TODO check
|
||||
self.trace_K = self.psi0 - np.trace(self.A)
|
||||
self.trace_K = self.psi0.sum() - np.trace(self.A)
|
||||
self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
|
||||
self.C = mdot(self.LLambdai, self.psi1V)
|
||||
self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
|
||||
|
|
@ -176,10 +202,15 @@ class sparse_GP(GP):
|
|||
Compute the (lower bound on the) log marginal likelihood
|
||||
"""
|
||||
beta_logdet = self.N*self.D*np.log(self.beta) if not self.EP else self.D*np.sum(np.log(self.beta))
|
||||
A = -0.5*self.N*self.D*(np.log(2.*np.pi)) - 0.5*beta_logdet
|
||||
B = -0.5*self.beta*self.D*self.trace_K if not self.EP else -0.5*self.D*self.trace_K
|
||||
if self.hetero_noise:
|
||||
A = foo
|
||||
B = bar
|
||||
D = -0.5*self.trbetaYYT
|
||||
else:
|
||||
A = -0.5*self.N*self.D*(np.log(2.*np.pi)) - 0.5*beta_logdet
|
||||
B = -0.5*self.beta*self.D*self.trace_K if not self.EP else -0.5*self.D*self.trace_K
|
||||
D = -0.5*self.beta*self.trYYT
|
||||
C = -0.5*self.D * self.B_logdet
|
||||
D = -0.5*self.beta*self.trYYT if not self.EP else -0.5*self.trbetaYYT
|
||||
E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
|
||||
return A+B+C+D+E
|
||||
|
||||
|
|
@ -243,13 +274,14 @@ class sparse_GP(GP):
|
|||
noise_term = 1./self.beta if not self.EP else 0
|
||||
Kxx = self.kern.Kdiag(Xnew)
|
||||
var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.LBL_inv, Kx),0) + noise_term
|
||||
return mu,var
|
||||
return mu,var,None#TODO add phi for EP
|
||||
|
||||
def plot(self, *args, **kwargs):
|
||||
"""
|
||||
Plot the fitted model: just call the GP_regression plot function and then add inducing inputs
|
||||
"""
|
||||
GP_regression.plot(self,*args,**kwargs)
|
||||
#GP_regression.plot(self,*args,**kwargs)
|
||||
GP.plot(self,*args,**kwargs)
|
||||
if self.Q==1:
|
||||
pb.plot(self.Z,self.Z*0+pb.ylim()[0],'k|',mew=1.5,markersize=12)
|
||||
if self.has_uncertain_inputs:
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue