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very basic functionality is now working
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James Hensman
parent
bdc89170d4
commit
d077d28fd1
10 changed files with 88 additions and 284 deletions
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@ -8,8 +8,6 @@ from .. import kern
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from ..core import model
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from ..util.linalg import pdinv,mdot
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from ..util.plot import gpplot, Tango
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from ..inference.EP import Full # TODO: tidy
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from ..inference import likelihoods
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class GP(model):
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"""
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@ -55,8 +53,6 @@ class GP(model):
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self._Xstd = np.ones((1,self.X.shape[1]))
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self.likelihood = likelihood
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self.Y = self.likelihood.Y
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self.YYT = self.likelihood.YYT # TODO: this is ugly. what about sufficient_stats?
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assert self.X.shape[0] == self.likelihood.Y.shape[0]
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self.N, self.D = self.likelihood.Y.shape
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@ -67,18 +63,16 @@ class GP(model):
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self.likelihood._set_params(p[self.kern.Nparam:])
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self.K = self.kern.K(self.X,slices1=self.Xslices)
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self.K += np.diag(self.likelihood_variance)
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self.K += self.likelihood.variance
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self.Ki, self.L, self.Li, self.K_logdet = pdinv(self.K)
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#the gradient of the likelihood wrt the covariance matrix
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if self.YYT is None:
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self._alpha = np.dot(self.Ki,self.Y)
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self._alpha2 = np.square(self._alpha)
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self.dL_dK = 0.5*(np.dot(self._alpha,self._alpha.T)-self.D*self.Ki)
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if self.likelihood.YYT is None:
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alpha = np.dot(self.Ki,self.likelihood.Y)
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self.dL_dK = 0.5*(np.dot(alpha,alpha.T)-self.D*self.Ki)
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else:
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tmp = mdot(self.Ki, self.YYT, self.Ki)
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self._alpha2 = np.diag(tmp)
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tmp = mdot(self.Ki, self.likelihood.YYT, self.Ki)
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self.dL_dK = 0.5*(tmp - self.D*self.Ki)
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def _get_params(self):
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@ -95,16 +89,15 @@ class GP(model):
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this function does nothing
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"""
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self.likelihood.fit(self.K)
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self.Y, self.YYT, self.likelihood_variance, self.likelihood_Z = self.likelihood.sufficient_stats() # TODO: just store these in the likelihood?
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def _model_fit_term(self):
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"""
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Computes the model fit using YYT if it's available
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"""
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if self.YYT is None:
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return -0.5*np.sum(np.square(np.dot(self.Li,self.Y)))
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if self.likelihood.YYT is None:
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return -0.5*np.sum(np.square(np.dot(self.Li,self.likelihood.Y)))
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else:
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return -0.5*np.sum(np.multiply(self.Ki, self.YYT))
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return -0.5*np.sum(np.multiply(self.Ki, self.likelihood.YYT))
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def log_likelihood(self):
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"""
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@ -114,7 +107,7 @@ class GP(model):
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model for a new variable Y* = v_tilde/tau_tilde, with a covariance
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matrix K* = K + diag(1./tau_tilde) plus a normalization term.
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"""
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return -0.5*self.D*self.K_logdet + self.model_fit_term() + self.likelihood.Z
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return -0.5*self.D*self.K_logdet + self._model_fit_term() + self.likelihood.Z
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def _log_likelihood_gradients(self):
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@ -125,7 +118,7 @@ class GP(model):
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For the likelihood parameters, pass in alpha = K^-1 y
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"""
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return np.hstack((self.kern.dK_dtheta(partial=self.dL_dK(),X=self.X), self.likelihood._gradients(self.alpha2)))
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return np.hstack((self.kern.dK_dtheta(partial=self.dL_dK,X=self.X), self.likelihood._gradients(partial=self.dL_dK)))
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def _raw_predict(self,_Xnew,slices, full_cov=False):
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"""
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@ -133,7 +126,7 @@ class GP(model):
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for normalisation or likelihood
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"""
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Kx = self.kern.K(self.X,_Xnew, slices1=self.Xslices,slices2=slices)
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mu = np.dot(np.dot(Kx.T,self.Ki),self.Y)
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mu = np.dot(np.dot(Kx.T,self.Ki),self.likelihood.Y)
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KiKx = np.dot(self.Ki,Kx)
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if full_cov:
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Kxx = self.kern.K(_Xnew, slices1=slices,slices2=slices)
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@ -177,8 +170,10 @@ class GP(model):
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return mean, _5pc, _95pc
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def plot(self,samples=0,plot_limits=None,which_data='all',which_functions='all',resolution=None,full_cov=False):
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def raw_plot(self,samples=0,plot_limits=None,which_data='all',which_functions='all',resolution=None):
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"""
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Plot the GP's view of the world, where the data is normalised and the likelihood is Gaussian
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:param samples: the number of a posteriori samples to plot
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:param which_data: which if the training data to plot (default all)
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:type which_data: 'all' or a slice object to slice self.X, self.Y
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@ -194,19 +189,17 @@ class GP(model):
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Can plot only part of the data and part of the posterior functions using which_data and which_functions
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"""
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if which_functions=='all':
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which_functions = [True]*self.kern.Nparts
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if which_data=='all':
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which_data = slice(None)
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X = self.X[which_data,:]
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Y = self.Y[which_data,:]
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Xorig = X*self._Xstd + self._Xmean
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Yorig = Y*self._Ystd + self._Ymean #NOTE For EP this is v_tilde/beta
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Y = self.likelihood.Y[which_data,:]
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if plot_limits is None:
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xmin,xmax = Xorig.min(0),Xorig.max(0)
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xmin,xmax = X.min(0),X.max(0)
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xmin, xmax = xmin-0.2*(xmax-xmin), xmax+0.2*(xmax-xmin)
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elif len(plot_limits)==2:
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xmin, xmax = plot_limits
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@ -215,27 +208,17 @@ class GP(model):
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if self.X.shape[1]==1:
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Xnew = np.linspace(xmin,xmax,resolution or 200)[:,None]
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m,v,phi = self.predict(Xnew,slices=which_functions,full_cov=full_cov)
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if self.EP:
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pb.subplot(211)
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gpplot(Xnew,m,v)
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m,v = self._raw_predict(Xnew,slices=which_functions,full_cov=False)
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lower, upper = m.flatten() - 2.*np.sqrt(v) , m.flatten()+ 2.*np.sqrt(v)
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gpplot(Xnew,m,lower,upper)
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if samples: #NOTE why don't we put samples as a parameter of gpplot
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s = np.random.multivariate_normal(m.flatten(),np.diag(v.flatten()),samples)
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pb.plot(Xnew.flatten(),s.T, alpha = 0.4, c='#3465a4', linewidth = 0.8)
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pb.plot(Xorig,Yorig,'kx',mew=1.5)
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pb.plot(X,Y,'kx',mew=1.5)
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pb.xlim(xmin,xmax)
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if self.EP:
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pb.subplot(212)
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self.likelihood.plot(Xnew,m,v,phi,self.X,samples=samples)
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pb.xlim(xmin,xmax)
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elif self.X.shape[1]==2:
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resolution = 50 or resolution
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resolution = resolution or 50
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xx,yy = np.mgrid[xmin[0]:xmax[0]:1j*resolution,xmin[1]:xmax[1]:1j*resolution]
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Xtest = np.vstack((xx.flatten(),yy.flatten())).T
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zz,vv,phi = self.predict(Xtest,slices=which_functions,full_cov=full_cov)
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zz,vv = self._raw_predict(Xtest,slices=which_functions,full_cov=False)
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zz = zz.reshape(resolution,resolution)
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pb.contour(xx,yy,zz,vmin=zz.min(),vmax=zz.max(),cmap=pb.cm.jet)
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pb.scatter(Xorig[:,0],Xorig[:,1],40,Yorig,linewidth=0,cmap=pb.cm.jet,vmin=zz.min(),vmax=zz.max())
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@ -244,3 +227,10 @@ class GP(model):
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else:
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raise NotImplementedError, "Cannot plot GPs with more than two input dimensions"
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def plot(self):
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"""
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Plot the data's view of the world, with non-normalised values and GP predictions passed through the likelihood
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"""
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pass# TODO!!!!!
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