mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-05-18 13:55:14 +02:00
Other changes.
This commit is contained in:
Ricardo Andrade
parent
fad0e07624
commit
29ec128c9d
7 changed files with 164 additions and 143 deletions
|
|
@ -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:
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue