generalized fitc + examples

GPy/examples/fitc_class_01.py

@@ -0,0 +1,53 @@
+import pylab as pb
+import numpy as np
+import GPy
+pb.ion()
+pb.close('all')
+
+"""
+Simple 1D classification example
+:param seed : seed value for data generation (default is 4).
+:type seed: int
+"""
+seed=10000
+
+data = GPy.util.datasets.toy_linear_1d_classification(seed=seed)
+X = data['X']
+Y = data['Y'][:, 0:1]
+Y[Y == -1] = 0
+
+
+
+#X = np.vstack((np.random.uniform(0,10,(10,1)),np.random.uniform(7,17,(10,1)),np.random.uniform(15,25,(10,1))))
+#Y = np.vstack((np.zeros((10,1)),np.ones((10,1)),np.zeros((10,1))))
+
+# Kernel object
+kernel = GPy.kern.rbf(1) + GPy.kern.white(1)
+
+# Likelihood object
+distribution = GPy.likelihoods.likelihood_functions.probit()
+likelihood = GPy.likelihoods.EP(Y,distribution)
+
+Z = np.random.uniform(X.min(),X.max(),(10,1))
+#Z = np.array([0,20])[:,None]
+print Z
+
+# Model definition
+m = GPy.models.generalized_FITC(X,likelihood=likelihood,kernel=kernel,Z=Z,normalize_X=False)
+m.set('len',2.)
+
+m.ensure_default_constraints()
+# Optimize
+#m.constrain_fixed('iip')
+m.update_likelihood_approximation()
+print m.checkgrad(verbose=1)
+# Parameters optimization:
+m.optimize()
+#m.EPEM() #FIXME
+
+# Plot
+pb.subplot(211)
+m.plot_f()
+pb.subplot(212)
+m.plot()
+print(m)

GPy/examples/fitc_class_02.py

@@ -0,0 +1,66 @@
+import pylab as pb
+import numpy as np
+import GPy
+pb.close('all')
+
+seed=10000
+"""Run a Gaussian process classification on the crescent data. The demonstration calls the basic GP classification model and uses EP to approximate the likelihood.
+
+:param model_type: type of model to fit ['Full', 'FITC', 'DTC'].
+:param seed : seed value for data generation.
+:type seed: int
+:param inducing : number of inducing variables (only used for 'FITC' or 'DTC').
+:type inducing: int
+"""
+
+data = GPy.util.datasets.crescent_data(seed=seed)
+
+# Kernel object
+kernel = GPy.kern.rbf(data['X'].shape[1]) + GPy.kern.white(data['X'].shape[1])
+
+# Likelihood object
+distribution = GPy.likelihoods.likelihood_functions.probit()
+likelihood = GPy.likelihoods.EP(data['Y'],distribution)
+
+sample = np.random.randint(0,data['X'].shape[0],10)
+Z = data['X'][sample,:]
+# create sparse GP EP model
+#m = GPy.models.sparse_GP(data['X'],likelihood=likelihood,kernel=kernel,Z=Z)
+m = GPy.models.generalized_FITC(data['X'],likelihood=likelihood,kernel=kernel,Z=Z)
+m.ensure_default_constraints()
+m.set('len',10.)
+
+m.update_likelihood_approximation()
+
+# optimize
+m.optimize()
+print(m)
+
+# plot
+m.plot()
+fitc = m
+
+pb.figure()
+# Kernel object
+kernel = GPy.kern.rbf(data['X'].shape[1]) + GPy.kern.white(data['X'].shape[1])
+
+# Likelihood object
+distribution = GPy.likelihoods.likelihood_functions.probit()
+likelihood = GPy.likelihoods.EP(data['Y'],distribution)
+
+sample = np.random.randint(0,data['X'].shape[0],10)
+Z = data['X'][sample,:]
+# create sparse GP EP model
+m = GPy.models.sparse_GP(data['X'],likelihood=likelihood,kernel=kernel,Z=Z)
+m.ensure_default_constraints()
+m.set('len',10.)
+
+m.update_likelihood_approximation()
+
+# optimize
+m.optimize()
+print(m)
+
+# plot
+m.plot()
+variational = m

GPy/examples/fitc_regr_01.py

@@ -0,0 +1,53 @@
+import pylab as pb
+import numpy as np
+import GPy
+pb.ion()
+pb.close('all')
+
+N = 400
+M = 10
+# sample inputs and outputs
+X = np.random.uniform(-3.,3.,(N,1))
+Y = np.sin(X)+np.random.randn(N,1)*0.05
+
+"""Run a 1D example of a sparse GP regression."""
+"""
+rbf =  GPy.kern.rbf(1)
+noise = GPy.kern.white(1)
+kernel = rbf + noise
+Z = np.random.uniform(-3,3,(M,1))
+likelihood = GPy.likelihoods.Gaussian(Y)
+m = GPy.models.sparse_GP(X, likelihood, kernel, Z)
+m.scale_factor=10000
+m.constrain_positive('(variance|lengthscale|precision)')
+m.checkgrad(verbose=1)
+m.optimize('tnc', messages = 1)
+pb.figure()
+m.plot()
+
+variational = m
+"""
+
+# construct kernel
+rbf =  GPy.kern.rbf(1)
+noise = GPy.kern.white(1)
+kernel = rbf + noise
+#Z = np.random.uniform(-3,3,(M,1))
+Z = variational.Z
+likelihood = GPy.likelihoods.Gaussian(Y)
+# create simple GP model
+m = GPy.models.generalized_FITC(X, likelihood, kernel, Z=Z)
+m.constrain_positive('(variance|lengthscale|precision)')
+#m.constrain_fixed('iip')
+m.checkgrad(verbose=1)
+m.optimize('tnc', messages = 1)
+#pb.figure()
+#m.plot()
+"""
+Xnew = X.copy().flatten()
+Xnew.sort()
+Xnew = Xnew[:,None]
+mean,var,low,up = m.predict(Xnew)
+GPy.util.plot.gpplot(Xnew,mean,low,up)
+fitc = m
+"""

GPy/models/generalized_FITC.py

@@ -32,14 +32,8 @@ class generalized_FITC(sparse_GP):
 
     def __init__(self, X, likelihood, kernel, Z, X_uncertainty=None, Xslices=None,Zslices=None, normalize_X=False):
 
-        if type(Z) == int:
+        self.Z = Z
-            #FIXME
+        self.M = self.Z.shape[0]
-            self.M = Z
-            self.Z = (np.random.random_sample(self.D*self.M)*(self.X.max()-self.X.min())+self.X.min()).reshape(self.M,-1)
-        elif type(Z) == np.ndarray:
-            self.Z = Z
-            self.M = self.Z.shape[0]
-
         self._precision = likelihood.precision
 
         sparse_GP.__init__(self, X, likelihood, kernel=kernel, Z=self.Z, X_uncertainty=None, Xslices=None,Zslices=None, normalize_X=False)
@@ -64,25 +58,26 @@ class generalized_FITC(sparse_GP):
         else:
             self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
             self._precision = self.likelihood.precision # Save the true precision
-            self.likelihood.precision = self.likelihood.precision/(1. + self.likelihood.precision*self.Diag0[:,None]) # Add the diagonal element of the FITC approximation
+            self.likelihood.precision = self._precision/(1. + self._precision*self.Diag0[:,None]) # Add the diagonal element of the FITC approximation
             self._set_params(self._get_params()) # update the GP
 
-
     def _FITC_computations(self):
         """
         FITC approximation doesn't have the correction term in the log-likelihood bound,
-        but adds a diagonal term to the covariance matrix.
+        but adds a diagonal term to the covariance matrix: diag(Knn - Qnn).
         This function:
-            - computes the diagonal term
+            - computes the FITC diagonal term
-            - eliminates the extra terms computed in the sparse_GP approximation
+            - removes the extra terms computed in the sparse_GP approximation
             - computes the likelihood gradients wrt the true precision.
         """
+        #NOTE the true precison is now '_precison' not 'precision'
         if self.likelihood.is_heteroscedastic:
+
             # Compute generalized FITC's diagonal term of the covariance
             self.Qnn = mdot(self.psi1.T,self.Kmmi,self.psi1)
             self.Diag0 = self.psi0 - np.diag(self.Qnn)
-
             self.Diag = self.Diag0/(1.+ self.Diag0 * self._precision.flatten())
+
             self.P = (self.Diag / self.Diag0)[:,None] * self.psi1.T
             self.RPT0 = np.dot(self.Lmi,self.psi1)
             self.L = np.linalg.cholesky(np.eye(self.M) + np.dot(self.RPT0,(1./self.Diag0 - self.Diag/(self.Diag0**2))[:,None]*self.RPT0.T))
@@ -92,14 +87,13 @@ class generalized_FITC(sparse_GP):
             self.w = self.Diag * self.likelihood.v_tilde
             self.gamma = np.dot(self.R.T, np.dot(self.RPT,self.likelihood.v_tilde))
             self.mu = self.w + np.dot(self.P,self.gamma)
-            self.mu_tilde = (self.likelihood.v_tilde/self.likelihood.tau_tilde)[:,None]
 
             # Remove extra term from dL_dpsi1
             self.dL_dpsi1 += -mdot(self.Kmmi,self.psi1*self.likelihood.precision.flatten().reshape(1,self.N)) #dB
         else:
+            raise NotImplementedError, "homoscedastic fitc not implemented"
             # Remove extra term from dL_dpsi1
-            self.dL_dpsi1 += -mdot(self.Kmmi,self.psi1*self.likelihood.precision) #dB
+            #self.dL_dpsi1 += -mdot(self.Kmmi,self.psi1*self.likelihood.precision) #dB
-
 
         sf = self.scale_factor
         sf2 = sf**2
@@ -110,18 +104,16 @@ class generalized_FITC(sparse_GP):
 
         #the partial derivative vector for the likelihood
         if self.likelihood.Nparams == 0:
-            #save computation here.
             self.partial_for_likelihood = None
         elif self.likelihood.is_heteroscedastic:
-            raise NotImplementedError, "heteroscedatic derivates not implemented"
+            raise NotImplementedError, "heteroscedastic derivates not implemented"
         else:
+            raise NotImplementedError, "homoscedastic derivatives not implemented"
             #likelihood is not heterscedatic
-            self.partial_for_likelihood =   - 0.5 * self.N*self.D*self._precision + 0.5 * np.sum(np.square(self.likelihood.Y))*self._precision**2
+            #self.partial_for_likelihood =   - 0.5 * self.N*self.D*self.likelihood.precision + 0.5 * np.sum(np.square(self.likelihood.Y))*self.likelihood.precision**2
-            self.partial_for_likelihood += 0.5 * self.D * trace_dot(self.Bi,self.A)*self._precision
+            #self.partial_for_likelihood += 0.5 * self.D * trace_dot(self.Bi,self.A)*self.likelihood.precision
-            self.partial_for_likelihood += self._precision*(0.5*trace_dot(self.psi2_beta_scaled,self.E*sf2) - np.trace(self.Cpsi1VVpsi1))
+            #self.partial_for_likelihood += self.likelihood.precision*(0.5*trace_dot(self.psi2_beta_scaled,self.E*sf2) - np.trace(self.Cpsi1VVpsi1))
-
         #TODO partial derivative vector for the likelihood not implemented
-        #NOTE the true precison is now '_precison' not 'precision'
 
     def dL_dtheta(self):
         """
@@ -147,23 +139,15 @@ class generalized_FITC(sparse_GP):
         D = 0.5*np.trace(self.Cpsi1VVpsi1)
         return A+C+D
 
-    def _raw_predict(self, Xnew, slices, full_cov=True):
+    def _raw_predict(self, Xnew, slices, full_cov=False):
         if self.likelihood.is_heteroscedastic:
             """
-            Make a prediction for the vsGP model
+            Make a prediction for the generalized FITC model
 
             Arguments
             ---------
             X : Input prediction data - Nx1 numpy array (floats)
             """
-            Kx = self.kern.K(self.Z, Xnew)
-            if full_cov:
-                Kxx = self.kern.K(Xnew)
-            else:
-                Kxx = self.kern.K(Xnew)#FIXME
-                #raise NotImplementedError
-                #Kxx = self.kern.Kdiag(Xnew)
-
             # q(u|f) = N(u| R0i*mu_u*f, R0i*C*R0i.T)
 
             # Ci = I + (RPT0)Di(RPT0).T
@@ -184,13 +168,19 @@ class generalized_FITC(sparse_GP):
             self.mu_H = mu_H
             Sigma_H = C + np.dot(mu_u,np.dot(self.Sigma,mu_u.T))
             # q(f_star|y) = N(f_star|mu_star,sigma2_star)
+            Kx = self.kern.K(self.Z, Xnew)
             KR0T = np.dot(Kx.T,self.Lmi.T)
             mu_star = np.dot(KR0T,mu_H)
-            sigma2_star = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T))
+            if full_cov:
-            vdiag = np.diag(sigma2_star)
+                Kxx = self.kern.K(Xnew)
-            return mu_star[:,None],vdiag[:,None]
+                var = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T))
-        else:
+            else:
-            """Internal helper function for making predictions, does not account for normalization"""
+                Kxx = self.kern.Kdiag(Xnew)
+                Kxx_ = self.kern.K(Xnew)
+                var_ = Kxx_ + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T))
+                var = (Kxx + np.sum(KR0T.T*np.dot(Sigma_H - np.eye(self.M),KR0T.T),0))[:,None]
+            return mu_star[:,None],var
+            """
             Kx = self.kern.K(self.Z, Xnew)
             mu = mdot(Kx.T, self.C/self.scale_factor, self.psi1V)
             if full_cov:
@@ -199,5 +189,19 @@ class generalized_FITC(sparse_GP):
             else:
                 Kxx = self.kern.Kdiag(Xnew)
                 var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.C/self.scale_factor**2, Kx),0)
-
+            a = kjk
             return mu,var[:,None]
+            """
+        else:
+            raise NotImplementedError, "homoscedastic fitc not implemented"
+            """
+            Kx = self.kern.K(self.Z, Xnew)
+            mu = mdot(Kx.T, self.C/self.scale_factor, self.psi1V)
+            if full_cov:
+                Kxx = self.kern.K(Xnew)
+                var = Kxx - mdot(Kx.T, (self.Kmmi - self.C/self.scale_factor**2), Kx) #NOTE this won't work for plotting
+            else:
+                Kxx = self.kern.Kdiag(Xnew)
+                var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.C/self.scale_factor**2, Kx),0)
+            return mu,var[:,None]
+            """