mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-05-04 09:12:38 +02:00
Merge branch 'newGP' of github.com:SheffieldML/GPy into newGP
This commit is contained in:
Alan Saul
commit
6b62ae960a
6 changed files with 163 additions and 170 deletions
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@ -43,6 +43,6 @@ print m.checkgrad()
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# Optimize and plot
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m.optimize()
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#m.em(plot_all=False) # EM algorithm
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m.plot()
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m.plot(samples=4)
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print(m)
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@ -14,6 +14,7 @@ pb.ion()
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N = 500
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M = 5
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pb.close('all')
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######################################
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## 1 dimensional example
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@ -31,18 +32,29 @@ noise = GPy.kern.white(1)
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kernel = rbf + noise
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# create simple GP model
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#m1 = GPy.models.sparse_GP(X, Y, kernel, M=M)
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m1 = GPy.models.sparse_GP(X,Y=None, kernel=kernel, M=M,likelihood= likelihood)
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#m = GPy.models.sparse_GP(X,Y=None, kernel=kernel, M=M,likelihood= likelihood)
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print m1.checkgrad()
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# contrain all parameters to be positive
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m1.constrain_positive('(variance|lengthscale|precision)')
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#m1.constrain_positive('(variance|lengthscale)')
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#m1.constrain_fixed('prec',10.)
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#m.constrain_fixed('prec',100.)
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m = GPy.models.sparse_GP(X, Y, kernel, M=M)
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m.ensure_default_constraints()
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#if not isinstance(m.likelihood,GPy.inference.likelihoods.gaussian):
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# m.approximate_likelihood()
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print m.checkgrad()
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m.optimize('tnc', messages = 1)
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m.plot(samples=3)
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print m
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#check gradient FIXME unit test please
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# optimize and plot
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m1.optimize('tnc', messages = 1)
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m1.plot()
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# print(m1)
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n = GPy.models.sparse_GP(X,Y=None, kernel=kernel, M=M,likelihood= likelihood)
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n.ensure_default_constraints()
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if not isinstance(n.likelihood,GPy.inference.likelihoods.gaussian):
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n.approximate_likelihood()
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print n.checkgrad()
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pb.figure()
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n.plot()
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"""
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m = GPy.models.sparse_GP_regression(X, Y, kernel, M=M)
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m.ensure_default_constraints()
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print m.checkgrad()
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"""
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@ -136,7 +136,7 @@ class DTC(EP):
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q(f|X) = int_{df}{N(f|KfuKuu_invu,diag(Kff-Qff)*N(u|0,Kuu)} = N(f|0,Sigma0)
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Sigma0 = Qnn = Knm*Kmmi*Kmn
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"""
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self.Kmmi, self.Kmm_hld = pdinv(self.Kmm)
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self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
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self.KmnKnm = np.dot(self.Kmn, self.Kmn.T)
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self.KmmiKmn = np.dot(self.Kmmi,self.Kmn)
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self.Qnn_diag = np.sum(self.Kmn*self.KmmiKmn,-2)
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@ -222,7 +222,7 @@ class FITC(EP):
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q(f|X) = int_{df}{N(f|KfuKuu_invu,diag(Kff-Qff)*N(u|0,Kuu)} = N(f|0,Sigma0)
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Sigma0 = diag(Knn-Qnn) + Qnn, Qnn = Knm*Kmmi*Kmn
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"""
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self.Kmmi, self.Kmm_hld = pdinv(self.Kmm)
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self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
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self.P0 = self.Kmn.T
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self.KmnKnm = np.dot(self.P0.T, self.P0)
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self.KmmiKmn = np.dot(self.Kmmi,self.P0.T)
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@ -83,12 +83,20 @@ class probit(likelihood):
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var = var.flatten()
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return stats.norm.cdf(mu/np.sqrt(1+var))
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def predictive_var(self,mu,var):
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p=self.predictive_mean(mu,var)
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return p*(1-p)
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def _log_likelihood_gradients():
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raise NotImplementedError
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def plot(self,X,phi,X_obs,Z=None):
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def plot(self,X,mu,var,phi,X_obs,Z=None,samples=0):
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assert X_obs.shape[1] == 1, 'Number of dimensions must be 1'
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gpplot(X,phi,np.zeros(X.shape[0]))
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phi_var = self.predictive_var(mu,var)
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gpplot(X,phi,phi_var)
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if samples:
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phi_samples = np.vstack([np.random.binomial(1,phi.flatten()) for s in range(samples)])
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pb.plot(X,phi_samples.T,'x', alpha = 0.4, c='#3465a4' )
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pb.plot(X_obs,(self.Y+1)/2,'kx',mew=1.5)
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if Z is not None:
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pb.plot(Z,Z*0+.5,'r|',mew=1.5,markersize=12)
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@ -164,16 +172,22 @@ class poisson(likelihood):
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sigma2_hat = m2 - mu_hat**2 # Second central moment
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return float(Z_hat), float(mu_hat), float(sigma2_hat)
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def predictive_mean(self,mu,variance):
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def predictive_mean(self,mu,var):
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return np.exp(mu*self.scale + self.location)
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def predictive_var(self,mu,var):
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return predictive_mean(mu,var)
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def _log_likelihood_gradients():
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raise NotImplementedError
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def plot(self,X,phi,X_obs,Z=None):
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def plot(self,X,mu,var,phi,X_obs,Z=None,samples=0):
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assert X_obs.shape[1] == 1, 'Number of dimensions must be 1'
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gpplot(X,phi,np.zeros(X.shape[0]))
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gpplot(X,phi,phi.flatten())
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pb.plot(X_obs,self.Y,'kx',mew=1.5)
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if samples:
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phi_samples = np.vstack([np.random.poisson(phi.flatten(),phi.size) for s in range(samples)])
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pb.plot(X,phi_samples.T, alpha = 0.4, c='#3465a4', linewidth = 0.8)
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if Z is not None:
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pb.plot(Z,Z*0+pb.ylim()[0],'k|',mew=1.5,markersize=12)
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@ -73,7 +73,6 @@ class GP(model):
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self.EP = False
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self.Y = Y
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self.beta = 100.#FIXME beta should be an explicit parameter for this model
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# Here's some simple normalisation
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if normalize_Y:
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self._Ymean = Y.mean(0)[None,:]
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@ -88,8 +87,9 @@ class GP(model):
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self.YYT = np.dot(self.Y, self.Y.T)
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else:
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self.YYT = None
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else:
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if self.D > 1:
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raise NotImplementedError, "EP is not implemented for D > 1"
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# Y is defined after approximating the likelihood
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self.EP = True
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self.eta,self.delta = power_ep
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@ -196,7 +196,6 @@ class GP(model):
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This is to allow for different normalisations of the output dimensions.
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"""
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#normalise X values
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Xnew = (Xnew.copy() - self._Xmean) / self._Xstd
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mu, var, phi = self._raw_predict(Xnew, slices, full_cov)
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@ -224,13 +223,18 @@ class GP(model):
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if full_cov:
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Kxx = self.kern.K(_Xnew, slices1=slices,slices2=slices)
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var = Kxx - np.dot(KiKx.T,Kx)
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if self.EP:
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raise NotImplementedError, "full_cov = True not implemented for EP"
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#var = np.diag(var)[:,None]
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#phi = self.likelihood.predictive_mean(mu,var)
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else:
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Kxx = self.kern.Kdiag(_Xnew, slices=slices)
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var = Kxx - np.sum(np.multiply(KiKx,Kx),0)
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phi = None if not self.EP else self.likelihood.predictive_mean(mu,var)
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if self.EP:
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phi = self.likelihood.predictive_mean(mu,var)
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return mu, var, phi
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def plot(self,samples=0,plot_limits=None,which_data='all',which_functions='all',resolution=None):
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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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"""
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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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@ -268,27 +272,27 @@ 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)
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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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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),samples)
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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.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,phi,self.X)
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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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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)
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zz,vv,phi = self.predict(Xtest,slices=which_functions,full_cov=full_cov)
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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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@ -7,9 +7,10 @@ from ..util.linalg import mdot, jitchol, chol_inv, pdinv
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from ..util.plot import gpplot
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from .. import kern
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from GP import GP
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from ..inference.EP import Full
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from ..inference.EP import Full,DTC,FITC
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from ..inference.likelihoods import likelihood,probit,poisson,gaussian
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#Still TODO:
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# make use of slices properly (kernel can now do this)
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# enable heteroscedatic noise (kernel will need to compute psi2 as a (NxMxM) array)
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@ -35,10 +36,6 @@ class sparse_GP(GP):
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:type beta: float
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:param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
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:type normalize_(X|Y): bool
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:parm likelihood: a GPy likelihood, defaults to gaussian
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:param epsilon_ep: convergence criterion for the Expectation Propagation algorithm, defaults to 0.1
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:param powerep: power-EP parameters [$\eta$,$\delta$], defaults to [1.,1.]
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:type powerep: list
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"""
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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,power_ep=[1.,1.]):
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@ -58,140 +55,32 @@ class sparse_GP(GP):
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self.X_uncertainty = X_uncertainty
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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)
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self.trYYT = np.sum(np.square(self.Y)) if not self.EP else None
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#normalise X uncertainty also
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if self.has_uncertain_inputs:
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self.X_uncertainty /= np.square(self._Xstd)
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if not self.EP:
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self.trYYT = np.sum(np.square(self.Y))
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else:
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self.method_ep = method_ep
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#normalise X uncertainty also
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if self.has_uncertain_inputs:
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self.X_uncertainty /= np.square(self._Xstd)
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def _set_params(self, p):
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self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
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if not self.EP:
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self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
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self.beta = p[self.M*self.Q]
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self.kern._set_params(p[self.Z.size + 1:])
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self.beta2 = self.beta**2
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self._compute_kernel_matrices()
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self._computations()
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else:
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self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
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self.kern._set_params(p[self.Z.size:])
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#self._compute_kernel_matrices() this is replaced by _ep_kernel_matrices
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self._ep_kernel_matrices()
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self._ep_computations()
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def _compute_kernel_matrices(self):
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# kernel computations, using BGPLVM notation
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#TODO: slices for psi statistics (easy enough)
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self.Kmm = self.kern.K(self.Z)
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if self.has_uncertain_inputs:
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if self.hetero_noise:
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raise NotImplementedError, "uncertain ips and het noise not yet supported"
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else:
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self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
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self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
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self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)
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else:
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if self.hetero_noise:
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print "rick's stuff here"
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else:
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self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices).sum()
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self.psi1 = self.kern.K(self.Z,self.X)
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self.psi2 = np.dot(self.psi1,self.psi1.T)
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def _computations(self):
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# TODO find routine to multiply triangular matrices
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self.V = self.beta*self.Y
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self.psi1V = np.dot(self.psi1, self.V)
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self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
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self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
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self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T)
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self.B = np.eye(self.M) + self.A
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self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
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self.LLambdai = np.dot(self.LBi, self.Lmi)
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self.trace_K = self.psi0 - np.trace(self.A)/self.beta
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self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
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self.C = mdot(self.LLambdai, self.psi1V)
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self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
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# Compute dL_dpsi
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self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
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self.dL_dpsi1 = mdot(self.LLambdai.T,self.C,self.V.T)
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self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
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# Compute dL_dKmm
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self.dL_dKmm = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi) # dB
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self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi) + self.Kmmi) # dC
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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
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def approximate_likelihood(self):
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assert not isinstance(self.likelihood, gaussian), "EP is only available for non-gaussian likelihoods"
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if self.ep_proxy == 'DTC':
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self.ep_approx = DTC(self.Kmm,self.likelihood,self.psi1,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
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elif self.ep_proxy == 'FITC':
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self.Knn_diag = self.kern.psi0(self.Z,self.X, self.X_uncertainty) #TODO psi0 already calculates this
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self.ep_approx = FITC(self.Kmm,self.likelihood,self.psi1,self.Knn_diag,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
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else:
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self.ep_approx = Full(self.X,self.likelihood,self.kernel,inducing=None,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
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self.beta, self.v_tilde, self.Z_hat, self.tau_, self.v_=self.ep_approx.fit_EP()
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self._ep_kernel_matrices()
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if self.Y is None:
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self.Y = np.ones([self.N,1])
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self._compute_kernel_matrices()
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self._computations()
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def _ep_kernel_matrices(self):
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self.Kmm = self.kern.K(self.Z)
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if self.has_uncertain_inputs:
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self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
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self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
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self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty) #FIXME include beta
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else:
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self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices)
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self.psi1 = self.kern.K(self.Z,self.X)
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self.psi2 = np.dot(self.psi1,self.psi1.T)
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self.psi2_beta_scaled = np.dot(self.psi1,self.beta*self.psi1.T)
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def _ep_computations(self):
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# Y: EP likelihood is defined as a regression model for mu_tilde
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self.Y = self.v_tilde/self.beta
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self._Ymean = np.zeros((1,self.Y.shape[1]))
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self._Ystd = np.ones((1,self.Y.shape[1]))
|
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self.trbetaYYT = np.sum(self.beta*np.square(self.Y))
|
||||
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_
|
||||
# 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_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.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)
|
||||
|
||||
# Compute dL_dpsi
|
||||
#self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
|
||||
self.dL_dpsi0 = - 0.5 * self.D * self.beta.flatten() * np.ones(self.N) #TODO check
|
||||
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)
|
||||
|
||||
# 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 _get_params(self):
|
||||
if not self.EP:
|
||||
return np.hstack([self.Z.flatten(),self.beta,self.kern._get_params_transformed()])
|
||||
|
|
@ -204,19 +93,84 @@ class sparse_GP(GP):
|
|||
else:
|
||||
return sum([['iip_%i_%i'%(i,j) for i in range(self.Z.shape[0])] for j in range(self.Z.shape[1])],[]) + self.kern._get_param_names_transformed()
|
||||
|
||||
|
||||
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 not self.EP:
|
||||
self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty)#.sum() NOTE psi0 is now a vector
|
||||
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)
|
||||
#self.psi2_beta_scaled = ?
|
||||
else:
|
||||
raise NotImplementedError, "uncertain_inputs not yet supported for EP"
|
||||
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)
|
||||
self.psi2_beta_scaled = np.dot(self.psi1,self.beta*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.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.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)
|
||||
self.trace_K_beta_scaled = (self.psi0*self.beta).sum() - np.trace(self.A)
|
||||
if not self.EP:
|
||||
self.trace_K = self.psi0.sum() - np.trace(self.A)/self.beta
|
||||
|
||||
# Compute dL_dpsi
|
||||
self.dL_dpsi1 = mdot(self.LLambdai.T,self.C,self.V.T)
|
||||
if not self.EP:
|
||||
self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
|
||||
if self.has_uncertain_inputs:
|
||||
self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
|
||||
else:
|
||||
self.dL_dpsi2_ = - 0.5 * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
|
||||
else:
|
||||
self.dL_dpsi0 = - 0.5 * self.D * self.beta.flatten()
|
||||
if not self.has_uncertain_inputs:
|
||||
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.*mdot(self.LBL_inv, self.psi2_beta_scaled, self.Kmmi) + self.Kmmi) # dC
|
||||
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.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.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()
|
||||
self.trbetaYYT = np.sum(np.square(self.Y)*self.beta)
|
||||
self._computations()
|
||||
|
||||
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
|
||||
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)))
|
||||
D = -0.5*self.trbetaYYT
|
||||
B = -0.5*self.D*self.trace_K_beta_scaled
|
||||
C = -0.5*self.D * self.B_logdet
|
||||
E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
|
||||
return A+B+C+D+E
|
||||
|
|
@ -246,7 +200,7 @@ class sparse_GP(GP):
|
|||
dL_dtheta += self.kern.dpsi2_dtheta(self.dL_dpsi2,self.Z,self.X, self.X_uncertainty) # for multiple_beta, dL_dpsi2 will be a different shape
|
||||
else:
|
||||
#re-cast computations in psi2 back to psi1:
|
||||
dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
|
||||
dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2_,self.beta.T*self.psi1) #dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
|
||||
dL_dtheta += self.kern.dK_dtheta(dL_dpsi1,self.Z,self.X)
|
||||
dL_dtheta += self.kern.dKdiag_dtheta(self.dL_dpsi0, self.X)
|
||||
|
||||
|
|
@ -262,32 +216,41 @@ class sparse_GP(GP):
|
|||
dL_dZ += self.kern.dpsi2_dZ(self.dL_dpsi2,self.Z,self.X, self.X_uncertainty)
|
||||
else:
|
||||
#re-cast computations in psi2 back to psi1:
|
||||
dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
|
||||
dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2_,self.beta.T*self.psi1)#dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
|
||||
dL_dZ += self.kern.dK_dX(dL_dpsi1,self.Z,self.X)
|
||||
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
|
||||
else:
|
||||
raise NotImplementedError, "full_cov = True not implemented for EP"
|
||||
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
|
||||
else:
|
||||
phi = self.likelihood.predictive_mean(mu,var)
|
||||
return mu,var,phi
|
||||
|
||||
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.plot(self,*args,**kwargs)
|
||||
if self.Q==1:
|
||||
pb.plot(self.Z,self.Z*0+pb.ylim()[0],'k|',mew=1.5,markersize=12)
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue