mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-06-05 14:55:15 +02:00
Other changes.
This commit is contained in:
Ricardo Andrade
parent
fad0e07624
commit
29ec128c9d
7 changed files with 164 additions and 143 deletions
|
|
@ -11,11 +11,9 @@ import GPy
|
|||
pb.ion()
|
||||
|
||||
pb.close('all')
|
||||
default_seed=10000
|
||||
|
||||
model_type='Full'
|
||||
inducing=4
|
||||
seed=default_seed
|
||||
"""Simple 1D classification example.
|
||||
:param model_type: type of model to fit ['Full', 'FITC', 'DTC'].
|
||||
:param seed : seed value for data generation (default is 4).
|
||||
|
|
@ -23,21 +21,19 @@ seed=default_seed
|
|||
:param inducing : number of inducing variables (only used for 'FITC' or 'DTC').
|
||||
:type inducing: int
|
||||
"""
|
||||
data = GPy.util.datasets.toy_linear_1d_classification(seed=seed)
|
||||
data = GPy.util.datasets.toy_linear_1d_classification(seed=0)
|
||||
likelihood = GPy.inference.likelihoods.probit(data['Y'][:, 0:1])
|
||||
|
||||
m = GPy.models.GP(data['X'],likelihood=likelihood)
|
||||
#m = GPy.models.GP(data['X'],Y=likelihood.Y)
|
||||
#m = GPy.models.GP(data['X'],likelihood.Y)
|
||||
|
||||
m.constrain_positive('var')
|
||||
m.constrain_positive('len')
|
||||
m.tie_param('lengthscale')
|
||||
m.ensure_default_constraints()
|
||||
if not isinstance(m.likelihood,GPy.inference.likelihoods.gaussian):
|
||||
m.approximate_likelihood()
|
||||
print m.checkgrad()
|
||||
# Optimize and plot
|
||||
m.optimize()
|
||||
#m.em(plot_all=False) # EM algorithm
|
||||
m.plot()
|
||||
m.plot(samples=3)
|
||||
|
||||
print(m)
|
||||
|
|
|
|||
|
|
@ -31,7 +31,7 @@ Y = F + E
|
|||
pb.plot(X,F,'k-')
|
||||
pb.plot(X,Y,'ro')
|
||||
pb.figure()
|
||||
likelihood = GPy.inference.likelihoods.poisson(Y,scale=4.)
|
||||
likelihood = GPy.inference.likelihoods.poisson(Y,scale=6.)
|
||||
|
||||
m = GPy.models.GP(X,likelihood=likelihood)
|
||||
#m = GPy.models.GP(data['X'],Y=likelihood.Y)
|
||||
|
|
|
|||
|
|
@ -31,46 +31,18 @@ noise = GPy.kern.white(1)
|
|||
kernel = rbf + noise
|
||||
|
||||
# create simple GP model
|
||||
#m1 = GPy.models.sparse_GP_regression(X, Y, kernel, M=M)
|
||||
m1 = GPy.models.sparse_GP(X, kernel, M=M,likelihood= likelihood)
|
||||
#m1 = GPy.models.sparse_GP(X, Y, kernel, M=M)
|
||||
m1 = GPy.models.sparse_GP(X,Y=None, kernel=kernel, M=M,likelihood= likelihood)
|
||||
|
||||
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.)
|
||||
|
||||
|
||||
#check gradient FIXME unit test please
|
||||
m1.checkgrad()
|
||||
# optimize and plot
|
||||
m1.optimize('tnc', messages = 1)
|
||||
m1.plot()
|
||||
# print(m1)
|
||||
|
||||
######################################
|
||||
## 2 dimensional example
|
||||
|
||||
# # sample inputs and outputs
|
||||
# X = np.random.uniform(-3.,3.,(N,2))
|
||||
# Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(N,1)*0.05
|
||||
|
||||
# # construct kernel
|
||||
# rbf = GPy.kern.rbf(2)
|
||||
# noise = GPy.kern.white(2)
|
||||
# kernel = rbf + noise
|
||||
|
||||
# # create simple GP model
|
||||
# m2 = GPy.models.sparse_GP_regression(X,Y,kernel, M = 50)
|
||||
# create simple GP model
|
||||
|
||||
# # contrain all parameters to be positive (but not inducing inputs)
|
||||
# m2.constrain_positive('(variance|lengthscale|precision)')
|
||||
|
||||
# #check gradient FIXME unit test please
|
||||
# m2.checkgrad()
|
||||
|
||||
# # optimize and plot
|
||||
# pb.figure()
|
||||
# m2.optimize('tnc', messages = 1)
|
||||
# m2.plot()
|
||||
# print(m2)
|
||||
|
|
|
|||
|
|
@ -110,7 +110,6 @@ class Full(EP):
|
|||
self.Sigma = self.Sigma - Delta_tau/(1.+ Delta_tau*self.Sigma[i,i])*np.dot(si,si.T)
|
||||
self.mu = np.dot(self.Sigma,self.v_tilde)
|
||||
self.iterations += 1
|
||||
print self.tau_tilde[i] #TODO erase me
|
||||
#Sigma recomptutation with Cholesky decompositon
|
||||
Sroot_tilde_K = np.sqrt(self.tau_tilde)[:,None]*(self.K)
|
||||
B = np.eye(self.N) + np.sqrt(self.tau_tilde)[None,:]*Sroot_tilde_K
|
||||
|
|
@ -122,7 +121,13 @@ class Full(EP):
|
|||
epsilon_np2 = sum((self.v_tilde-self.np2[-1])**2)/self.N
|
||||
self.np1.append(self.tau_tilde.copy())
|
||||
self.np2.append(self.v_tilde.copy())
|
||||
return self.tau_tilde[:,None], self.v_tilde[:,None], self.Z_hat[:,None], self.tau_[:,None], self.v_[:,None]
|
||||
|
||||
#Variables to be called from GP
|
||||
mu_tilde = self.v_tilde/self.tau_tilde #When calling EP, this variable is used instead of Y in the GP model
|
||||
sigma_sum = 1./self.tau_ + 1./self.tau_tilde
|
||||
mu_diff_2 = (self.v_/self.tau_ - mu_tilde)**2
|
||||
Z_ep = np.sum(np.log(self.Z_hat)) + 0.5*np.sum(np.log(sigma_sum)) + 0.5*np.sum(mu_diff_2/sigma_sum) #Normalization constant
|
||||
return self.tau_tilde[:,None], mu_tilde[:,None], Z_ep
|
||||
|
||||
class DTC(EP):
|
||||
def fit_EP(self):
|
||||
|
|
|
|||
|
|
@ -21,6 +21,27 @@ class likelihood:
|
|||
self.location = location
|
||||
self.scale = scale
|
||||
|
||||
def plot1D(self,X,mean,var,Z=None,mean_Z=None,var_Z=None,samples=0):
|
||||
"""
|
||||
Plot the predictive distribution of the GP model for 1-dimensional inputs
|
||||
|
||||
:param X: The points at which to make a prediction
|
||||
:param Mean: mean values at X
|
||||
:param Var: variance values at X
|
||||
:param Z: Set of points to be highlighted in the plot, i.e. inducing points
|
||||
:param mean_Z: mean values at Z
|
||||
:param var_Z: variance values at Z
|
||||
:samples: Number of samples to plot
|
||||
"""
|
||||
assert X.shape[1] == 1, 'Number of dimensions must be 1'
|
||||
gpplot(X,mean,var.flatten())
|
||||
if samples: #NOTE why don't we put samples as a parameter of gpplot
|
||||
s = np.random.multivariate_normal(mean.flatten(),np.diag(var),samples)
|
||||
pb.plot(X.flatten(),s.T, alpha = 0.4, c='#3465a4', linewidth = 0.8)
|
||||
#pb.subplot(211)
|
||||
#self.plot1Da(X,mean,var,Z,mean_Z,var_Z)
|
||||
|
||||
|
||||
def plot1Da(self,X,mean,var,Z=None,mean_Z=None,var_Z=None):
|
||||
"""
|
||||
Plot the predictive distribution of the GP model for 1-dimensional inputs
|
||||
|
|
@ -37,6 +58,7 @@ class likelihood:
|
|||
pb.errorbar(Z.flatten(),mean_Z.flatten(),2*np.sqrt(var_Z.flatten()),fmt='r+')
|
||||
pb.plot(Z,mean_Z,'ro')
|
||||
|
||||
"""
|
||||
def plot1Db(self,X_obs,X,phi,Z=None):
|
||||
assert X_obs.shape[1] == 1, 'Number of dimensions must be 1'
|
||||
gpplot(X,phi,np.zeros(X.shape[0]))
|
||||
|
|
@ -45,6 +67,7 @@ class likelihood:
|
|||
if Z is not None:
|
||||
pb.plot(Z,Z*0+.5,'r|',mew=1.5,markersize=12)
|
||||
|
||||
"""
|
||||
def plot2D(self,X,X_new,F_new,U=None):
|
||||
"""
|
||||
Predictive distribution of the fitted GP model for 2-dimensional inputs
|
||||
|
|
@ -98,7 +121,6 @@ class probit(likelihood):
|
|||
sigma2_hat = 1./tau_i - (phi/((tau_i**2+tau_i)*Z_hat))*(z+phi/Z_hat)
|
||||
return Z_hat, mu_hat, sigma2_hat
|
||||
|
||||
|
||||
def predictive_mean(self,mu,var):
|
||||
mu = mu.flatten()
|
||||
var = var.flatten()
|
||||
|
|
@ -107,6 +129,14 @@ class probit(likelihood):
|
|||
def _log_likelihood_gradients():
|
||||
raise NotImplementedError
|
||||
|
||||
def plot(self,X,phi,X_obs,Z=None):
|
||||
assert X_obs.shape[1] == 1, 'Number of dimensions must be 1'
|
||||
gpplot(X,phi,np.zeros(X.shape[0]))
|
||||
pb.plot(X_obs,(self.Y+1)/2,'kx',mew=1.5)
|
||||
if Z is not None:
|
||||
pb.plot(Z,Z*0+.5,'r|',mew=1.5,markersize=12)
|
||||
pb.ylim(-0.2,1.2)
|
||||
|
||||
class poisson(likelihood):
|
||||
"""
|
||||
Poisson likelihood
|
||||
|
|
|
|||
|
|
@ -24,13 +24,18 @@ class GP(model):
|
|||
:type normalize_Y: False|True
|
||||
:param Xslices: how the X,Y data co-vary in the kernel (i.e. which "outputs" they correspond to). See (link:slicing)
|
||||
:rtype: model object
|
||||
:parm likelihood: a GPy likelihood, defaults to gaussian
|
||||
: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
|
||||
|
||||
.. Note:: Multiple independent outputs are allowed using columns of Y
|
||||
|
||||
"""
|
||||
#TODO: make beta parameter explicit
|
||||
#TODO: when using EP, predict needs to return 3 values otherwise it just needs 2. At the moment predict returns 3 values in any case.
|
||||
|
||||
def __init__(self,X,Y=None,kernel=None,normalize_X=False,normalize_Y=False, Xslices=None,likelihood=None,epsilon_ep=1e-3,epsion_em=.1,power_ep=[1.,1.]):
|
||||
#TODO: make beta parameter explicit
|
||||
def __init__(self,X,Y=None,kernel=None,normalize_X=False,normalize_Y=False, Xslices=None,likelihood=None,epsilon_ep=1e-3,epsilon_em=.1,power_ep=[1.,1.]):
|
||||
|
||||
# parse arguments
|
||||
self.Xslices = Xslices
|
||||
|
|
@ -54,7 +59,6 @@ class GP(model):
|
|||
self._Xmean = np.zeros((1,self.X.shape[1]))
|
||||
self._Xstd = np.ones((1,self.X.shape[1]))
|
||||
|
||||
|
||||
# Y - likelihood related variables, these might change whether using EP or not
|
||||
if likelihood is None:
|
||||
assert Y is not None, "Either Y or likelihood must be defined"
|
||||
|
|
@ -68,8 +72,9 @@ class GP(model):
|
|||
if isinstance(self.likelihood,gaussian):
|
||||
self.EP = False
|
||||
self.Y = Y
|
||||
self.beta = 100.#FIXME beta should be an explicit parameter for this model
|
||||
|
||||
#here's some simple normalisation
|
||||
# Here's some simple normalisation
|
||||
if normalize_Y:
|
||||
self._Ymean = Y.mean(0)[None,:]
|
||||
self._Ystd = Y.std(0)[None,:]
|
||||
|
|
@ -89,50 +94,43 @@ class GP(model):
|
|||
self.EP = True
|
||||
self.eta,self.delta = power_ep
|
||||
self.epsilon_ep = epsilon_ep
|
||||
self.tau_tilde = np.ones([self.N,self.D])
|
||||
self.v_tilde = np.zeros([self.N,self.D])
|
||||
self.tau_ = np.ones([self.N,self.D])
|
||||
self.v_ = np.zeros([self.N,self.D])
|
||||
self.Z_hat = np.ones([self.N,self.D])
|
||||
self.beta = np.ones([self.N,self.D])
|
||||
self.Z_ep = 0
|
||||
self.Y = None
|
||||
self._Ymean = np.zeros((1,self.D))
|
||||
self._Ystd = np.ones((1,self.D))
|
||||
|
||||
model.__init__(self)
|
||||
|
||||
def _set_params(self,p):
|
||||
# TODO: remove beta when using EP
|
||||
# TODO: add beta when not using EP
|
||||
self.kern._set_params_transformed(p)
|
||||
if not self.EP:
|
||||
self.K = self.kern.K(self.X,slices1=self.Xslices)
|
||||
self.Ki, self.L, self.Li, self.K_logdet = pdinv(self.K)
|
||||
else:
|
||||
self._ep_covariance()
|
||||
self.K = self.kern.K(self.X,slices1=self.Xslices)
|
||||
if self.EP:
|
||||
self.K += np.diag(1./self.beta.flatten())
|
||||
#else:
|
||||
# self.beta = p[-1]
|
||||
self.Ki, self.L, self.Li, self.K_logdet = pdinv(self.K)
|
||||
|
||||
def _get_params(self):
|
||||
# TODO: remove beta when using EP
|
||||
# TODO: add beta when not using EP
|
||||
return self.kern._get_params_transformed()
|
||||
|
||||
def _get_param_names(self):
|
||||
# TODO: remove beta when using EP
|
||||
# TODO: add beta when not using EP
|
||||
return self.kern._get_param_names_transformed()
|
||||
|
||||
def approximate_likelihood(self):
|
||||
assert not isinstance(self.likelihood, gaussian), "EP is only available for non-gaussian likelihoods"
|
||||
self.ep_approx = Full(self.K,self.likelihood,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
|
||||
self.tau_tilde, self.v_tilde, self.Z_hat, self.tau_, self.v_=self.ep_approx.fit_EP()
|
||||
# Y: EP likelihood is defined as a regression model for mu_tilde
|
||||
self.Y = self.v_tilde/self.tau_tilde
|
||||
self._Ymean = np.zeros((1,self.Y.shape[1]))
|
||||
self._Ystd = np.ones((1,self.Y.shape[1]))
|
||||
self.ep_approx = Full(self.K,self.likelihood,epsilon = self.epsilon_ep,power_ep=[self.eta,self.delta])
|
||||
self.beta, self.Y, self.Z_ep = self.ep_approx.fit_EP()
|
||||
if self.D > self.N:
|
||||
# then it's more efficient to store YYT
|
||||
self.YYT = np.dot(self.Y, self.Y.T)
|
||||
else:
|
||||
self.YYT = None
|
||||
self.mu_ = self.v_/self.tau_
|
||||
self._ep_covariance()
|
||||
|
||||
def _ep_covariance(self):
|
||||
# Kernel plus noise variance term
|
||||
self.K = self.kern.K(self.X,slices1=self.Xslices) + np.diag(1./self.tau_tilde.flatten())
|
||||
self.K = self.kern.K(self.X,slices1=self.Xslices) + np.diag(1./self.beta.flatten())
|
||||
self.Ki, self.L, self.Li, self.K_logdet = pdinv(self.K)
|
||||
|
||||
def _model_fit_term(self):
|
||||
|
|
@ -144,25 +142,16 @@ class GP(model):
|
|||
else:
|
||||
return -0.5*np.sum(np.multiply(self.Ki, self.YYT))
|
||||
|
||||
def _normalization_term(self):
|
||||
"""
|
||||
Computes the marginal likelihood normalization constants
|
||||
"""
|
||||
sigma_sum = 1./self.tau_ + 1./self.tau_tilde
|
||||
mu_diff_2 = (self.mu_ - self.Y)**2
|
||||
penalty_term = np.sum(np.log(self.Z_hat))
|
||||
return penalty_term + 0.5*np.sum(np.log(sigma_sum)) + 0.5*np.sum(mu_diff_2/sigma_sum)
|
||||
|
||||
def log_likelihood(self):
|
||||
"""
|
||||
The log marginal likelihood for an EP model can be written as the log likelihood of
|
||||
a regression model for a new variable Y* = v_tilde/tau_tilde, with a covariance
|
||||
matrix K* = K + diag(1./tau_tilde) plus a normalization term.
|
||||
"""
|
||||
complexity_term = -0.5*self.D*self.Kplus_logdet
|
||||
normalization_term = 0 if self.EP == False else self.normalization_term()
|
||||
return complexity_term + normalization_term + self._model_fit_term()
|
||||
|
||||
L = -0.5*selff.D*self.K_logdet + self.model_fit_term()
|
||||
if self.EP:
|
||||
L += self.normalisation_term()
|
||||
return L
|
||||
|
||||
def log_likelihood(self):
|
||||
complexity_term = -0.5*self.N*self.D*np.log(2.*np.pi) - 0.5*self.D*self.K_logdet
|
||||
|
|
@ -174,7 +163,6 @@ class GP(model):
|
|||
dL_dK = 0.5*(np.dot(alpha,alpha.T)-self.D*self.Ki)
|
||||
else:
|
||||
dL_dK = 0.5*(mdot(self.Ki, self.YYT, self.Ki) - self.D*self.Ki)
|
||||
|
||||
return dL_dK
|
||||
|
||||
def _log_likelihood_gradients(self):
|
||||
|
|
@ -267,7 +255,7 @@ class GP(model):
|
|||
Y = self.Y[which_data,:]
|
||||
|
||||
Xorig = X*self._Xstd + self._Xmean
|
||||
Yorig = Y*self._Ystd + self._Ymean if not self.EP else self.likelihood.Y
|
||||
Yorig = Y*self._Ystd + self._Ymean #NOTE For EP this is v_tilde/beta
|
||||
|
||||
if plot_limits is None:
|
||||
xmin,xmax = Xorig.min(0),Xorig.max(0)
|
||||
|
|
@ -282,19 +270,17 @@ class GP(model):
|
|||
m,v,phi = self.predict(Xnew,slices=which_functions)
|
||||
if self.EP:
|
||||
pb.subplot(211)
|
||||
|
||||
gpplot(Xnew,m,v)
|
||||
if samples:
|
||||
s = np.random.multivariate_normal(m.flatten(),v,samples)
|
||||
pb.plot(Xnew.flatten(),s.T, alpha = 0.4, c='#3465a4', linewidth = 0.8)
|
||||
|
||||
if not self.EP:
|
||||
pb.plot(Xorig,Yorig,'kx',mew=1.5)
|
||||
pb.xlim(xmin,xmax)
|
||||
else:
|
||||
pb.xlim(xmin,xmax)
|
||||
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)
|
||||
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)
|
||||
|
||||
if self.EP:
|
||||
pb.subplot(212)
|
||||
self.likelihood.plot1Db(self.X,Xnew,phi)
|
||||
self.likelihood.plot(Xnew,phi,self.X)
|
||||
pb.xlim(xmin,xmax)
|
||||
|
||||
elif self.X.shape[1]==2:
|
||||
|
|
|
|||
|
|
@ -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