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Log-likelihood,predictions and plotting are working.

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Ricardo 2013-01-29 23:54:02 +00:00
parent bb1e0021d7
commit d1a0883c12
4 changed files with 64 additions and 56 deletions
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19
GPy/examples/sparse_ep_fix.py
View file

@ -31,18 +31,17 @@ noise = GPy.kern.white(1)
kernel = rbf + noise
# create simple GP model
#m1 = GPy.models.sparse_GP(X, Y, kernel, M=M)
m1 = GPy.models.sparse_GP(X,Y=None, kernel=kernel, M=M,likelihood= likelihood)
m = GPy.models.sparse_GP(X,Y=None, kernel=kernel, M=M,likelihood= likelihood)
#m = GPy.models.sparse_GP(X, Y, kernel, M=M)
print m1.checkgrad()
# contrain all parameters to be positive
m1.constrain_positive('(variance|lengthscale|precision)')
#m1.constrain_positive('(variance|lengthscale)')
#m1.constrain_fixed('prec',10.)
m.ensure_default_constraints()
if not isinstance(m.likelihood,GPy.inference.likelihoods.gaussian):
m.approximate_likelihood()
print m.checkgrad()
#check gradient FIXME unit test please
# optimize and plot
m1.optimize('tnc', messages = 1)
m1.plot()
# print(m1)
#m.optimize('tnc', messages = 1)
m.plot(samples=3,full_cov=False)
# print(m)

4
GPy/inference/EP.py
View file

@ -136,7 +136,7 @@ class DTC(EP):
q(f|X) = int_{df}{N(f|KfuKuu_invu,diag(Kff-Qff)*N(u|0,Kuu)} = N(f|0,Sigma0)
Sigma0 = Qnn = Knm*Kmmi*Kmn
"""
self.Kmmi, self.Kmm_hld = pdinv(self.Kmm)
self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
self.KmnKnm = np.dot(self.Kmn, self.Kmn.T)
self.KmmiKmn = np.dot(self.Kmmi,self.Kmn)
self.Qnn_diag = np.sum(self.Kmn*self.KmmiKmn,-2)
@ -222,7 +222,7 @@ class FITC(EP):
q(f|X) = int_{df}{N(f|KfuKuu_invu,diag(Kff-Qff)*N(u|0,Kuu)} = N(f|0,Sigma0)
Sigma0 = diag(Knn-Qnn) + Qnn, Qnn = Knm*Kmmi*Kmn
"""
self.Kmmi, self.Kmm_hld = pdinv(self.Kmm)
self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
self.P0 = self.Kmn.T
self.KmnKnm = np.dot(self.P0.T, self.P0)
self.KmmiKmn = np.dot(self.Kmmi,self.P0.T)

16
GPy/models/GP.py
View file

@ -196,7 +196,6 @@ class GP(model):
This is to allow for different normalisations of the output dimensions.
"""
#normalise X values
Xnew = (Xnew.copy() - self._Xmean) / self._Xstd
mu, var, phi = self._raw_predict(Xnew, slices, full_cov)
@ -224,13 +223,18 @@ class GP(model):
if full_cov:
Kxx = self.kern.K(_Xnew, slices1=slices,slices2=slices)
var = Kxx - np.dot(KiKx.T,Kx)
if self.EP:
raise NotImplementedError, "full_cov = True not implemented for EP"
#var = np.diag(var)[:,None]
#phi = self.likelihood.predictive_mean(mu,var)
else:
Kxx = self.kern.Kdiag(_Xnew, slices=slices)
var = Kxx - np.sum(np.multiply(KiKx,Kx),0)
phi = None if not self.EP else self.likelihood.predictive_mean(mu,var)
if self.EP:
phi = self.likelihood.predictive_mean(mu,var)
return mu, var, phi
def plot(self,samples=0,plot_limits=None,which_data='all',which_functions='all',resolution=None):
def plot(self,samples=0,plot_limits=None,which_data='all',which_functions='all',resolution=None,full_cov=False):
"""
:param samples: the number of a posteriori samples to plot
:param which_data: which if the training data to plot (default all)
@ -268,13 +272,13 @@ class GP(model):
if self.X.shape[1]==1:
Xnew = np.linspace(xmin,xmax,resolution or 200)[:,None]
m,v,phi = self.predict(Xnew,slices=which_functions)
m,v,phi = self.predict(Xnew,slices=which_functions,full_cov=full_cov)
if self.EP:
pb.subplot(211)
gpplot(Xnew,m,v)
if samples: #NOTE why don't we put samples as a parameter of gpplot
s = np.random.multivariate_normal(m.flatten(),np.diag(v),samples)
s = np.random.multivariate_normal(m.flatten(),np.diag(v.flatten()),samples)
pb.plot(Xnew.flatten(),s.T, alpha = 0.4, c='#3465a4', linewidth = 0.8)
pb.plot(Xorig,Yorig,'kx',mew=1.5)
pb.xlim(xmin,xmax)
@ -288,7 +292,7 @@ class GP(model):
resolution = 50 or resolution
xx,yy = np.mgrid[xmin[0]:xmax[0]:1j*resolution,xmin[1]:xmax[1]:1j*resolution]
Xtest = np.vstack((xx.flatten(),yy.flatten())).T
zz,vv,phi = self.predict(Xtest,slices=which_functions)
zz,vv,phi = self.predict(Xtest,slices=which_functions,full_cov=full_cov)
zz = zz.reshape(resolution,resolution)
pb.contour(xx,yy,zz,vmin=zz.min(),vmax=zz.max(),cmap=pb.cm.jet)
pb.scatter(Xorig[:,0],Xorig[:,1],40,Yorig,linewidth=0,cmap=pb.cm.jet,vmin=zz.min(),vmax=zz.max())

81
GPy/models/sparse_GP.py
View file

@ -7,7 +7,7 @@ from ..util.linalg import mdot, jitchol, chol_inv, pdinv
from ..util.plot import gpplot
from .. import kern
from GP import GP
from ..inference.EP import Full
from ..inference.EP import Full,DTC,FITC
from ..inference.likelihoods import likelihood,probit,poisson,gaussian
#Still TODO:
@ -36,6 +36,8 @@ class sparse_GP(GP):
:param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
:type normalize_(X|Y): bool
:parm likelihood: a GPy likelihood, defaults to gaussian
:param method_ep: sparse approximation used by Expectation Propagation algorithm, defaults to DTC
:type M: string (Full|DTC|FITC)
:param epsilon_ep: convergence criterion for the Expectation Propagation algorithm, defaults to 0.1
:param powerep: power-EP parameters [$\eta$,$\delta$], defaults to [1.,1.]
:type powerep: list
@ -58,17 +60,22 @@ class sparse_GP(GP):
self.X_uncertainty = X_uncertainty
GP.__init__(self, X=X, Y=Y, kernel=kernel, normalize_X=normalize_X, normalize_Y=normalize_Y,likelihood=likelihood,epsilon_ep=epsilon_ep,power_ep=power_ep)
self.trYYT = np.sum(np.square(self.Y)) if not self.EP else None
#normalise X uncertainty also
if self.has_uncertain_inputs:
self.X_uncertainty /= np.square(self._Xstd)
if not self.EP:
self.trYYT = np.sum(np.square(self.Y))
else:
self.method_ep = method_ep
def _set_params(self, p):
self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
if not self.EP:
#self.beta = p[self.M*self.Q]
self.beta = np.repeat(p[self.M*self.Q],self.N)[:,None]
self.beta = p[self.M*self.Q]
#self.beta = np.repeat(p[self.M*self.Q],self.N)[:,None]
self.kern._set_params(p[self.Z.size + 1:])
self.beta2 = self.beta**2
else:
@ -76,7 +83,7 @@ class sparse_GP(GP):
if self.Y is None:
self.Y = np.ones([self.N,1])
self._compute_kernel_matrices()
self._computations()
self._computations() #NOTE At this point computations of dL are not needed
def _get_params(self):
if not self.EP:
@ -123,24 +130,29 @@ class sparse_GP(GP):
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,1])
self.dL_dpsi0 = - 0.5 * self.D * self.beta.flatten() * 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)
#self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
self.dL_dpsi2 = - 0.5 * (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
#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 += -0.5 * self.D * (- self.LBL_inv - 2.*mdot(self.LBL_inv, self.psi2_beta_scaled, 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
self.dL_dKmm += np.dot(np.dot(self.G,self.psi2_beta_scaled) - 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':
if self.method_ep == 'DTC':
self.ep_approx = DTC(self.Kmm,self.likelihood,self.psi1,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
elif self.ep_proxy == 'FITC':
elif self.method_ep == 'FITC':
self.ep_approx = FITC(self.Kmm,self.likelihood,self.psi1,self.psi0,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
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.Y, self.Z_ep = self.ep_approx.fit_EP()
print "Aqui toy"
self.trbetaYYT = np.sum(np.square(self.Y)*self.beta)
self._computations()
def log_likelihood(self):
@ -149,30 +161,11 @@ class sparse_GP(GP):
"""
if not self.EP:
A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta))
D = -0.5*self.beta*self.trYYT
else:
A = -0.5*self.D*(self.N*np.log(2.*np.pi) - np.sum(np.log(self.beta)))
B = -0.5*self.D*self.trace_K
C = -0.5*self.D * self.B_logdet
D = -0.5*self.beta*self.trYYT
E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
return A+B+C+D+E
def log_likelihood(self):
"""
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))
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
B = -0.5*self.D*self.trace_K
C = -0.5*self.D * self.B_logdet
E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
return A+B+C+D+E
@ -223,21 +216,33 @@ class sparse_GP(GP):
return dL_dZ
def _log_likelihood_gradients(self):
return np.hstack([self.dL_dZ().flatten(), self.dL_dbeta(), self.dL_dtheta()])
if not self.EP:
return np.hstack([self.dL_dZ().flatten(), self.dL_dbeta(), self.dL_dtheta()])
else:
return np.hstack([self.dL_dZ().flatten(), self.dL_dtheta()])
def _raw_predict(self, Xnew, slices, full_cov=False):
"""Internal helper function for making predictions, does not account for normalisation"""
Kx = self.kern.K(self.Z, Xnew)
mu = mdot(Kx.T, self.LBL_inv, self.psi1V)
phi = None
if full_cov:
noise_term = np.eye(Xnew.shape[0])/self.beta if not self.EP else 0
Kxx = self.kern.K(Xnew)
var = Kxx - mdot(Kx.T, (self.Kmmi - self.LBL_inv), Kx) + noise_term
var = Kxx - mdot(Kx.T, (self.Kmmi - self.LBL_inv), Kx)
if not self.EP:
var += np.eye(Xnew.shape[0])/self.beta # TODO: This beta doesn't belong here in the EP case.
else:
raise NotImplementedError, "full_cov = True not implemented for EP"
#var = np.diag(var)[:,None]
#phi = self.likelihood.predictive_mean(mu,var)
else:
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,None#TODO add phi for EP
var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.LBL_inv, Kx),0)
if not self.EP:
var += 1./self.beta # TODO: This beta doesn't belong here in the EP case.
else:
phi = self.likelihood.predictive_mean(mu,var)
return mu,var,phi
def plot(self, *args, **kwargs):
"""