[GPU] partial implmented minibatch inference

GPy/inference/latent_function_inference/__init__.py

@@ -31,6 +31,7 @@ from GPy.inference.latent_function_inference.var_dtc import VarDTC
 from expectation_propagation import EP
 from dtc import DTC
 from fitc import FITC
+from var_dtc_parallel import VarDTC_minibatch
 
 # class FullLatentFunctionData(object):
 #

GPy/inference/latent_function_inference/posterior.py

@@ -81,7 +81,7 @@ class Posterior(object):
     def covariance(self):
         if self._covariance is None:
             #LiK, _ = dtrtrs(self.woodbury_chol, self._K, lower=1)
-            self._covariance = np.tensordot(np.dot(np.atleast_3d(self.woodbury_inv).T, self._K), self._K, [1,0]).T
+            self._covariance = self._K - np.tensordot(np.dot(np.atleast_3d(self.woodbury_inv).T, self._K), self._K, [1,0]).T
             #self._covariance = self._K - self._K.dot(self.woodbury_inv).dot(self._K)
         return self._covariance.squeeze()
 

GPy/inference/latent_function_inference/var_dtc_parallel.py

@@ -0,0 +1,282 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+from posterior import Posterior
+from ...util.linalg import jitchol, backsub_both_sides, tdot, dtrtrs
+from ...util import diag
+from ...core.parameterization.variational import VariationalPosterior
+import numpy as np
+from ...util.misc import param_to_array
+log_2_pi = np.log(2*np.pi)
+
+class VarDTC_minibatch(object):
+    """
+    An object for inference when the likelihood is Gaussian, but we want to do sparse inference.
+
+    The function self.inference returns a Posterior object, which summarizes
+    the posterior.
+
+    For efficiency, we sometimes work with the cholesky of Y*Y.T. To save repeatedly recomputing this, we cache it.
+
+    """
+    const_jitter = 1e-6
+    def __init__(self, batchsize, limit=1):
+        
+        self.batchsize = batchsize
+        
+        # Cache functions
+        from ...util.caching import Cacher
+        self.get_trYYT = Cacher(self._get_trYYT, limit)
+        self.get_YYTfactor = Cacher(self._get_YYTfactor, limit)
+        
+        self.midRes = {}
+        self.batch_pos = 0 # the starting position of the current mini-batch
+
+    def set_limit(self, limit):
+        self.get_trYYT.limit = limit
+        self.get_YYTfactor.limit = limit
+        
+    def _get_trYYT(self, Y):
+        return param_to_array(np.sum(np.square(Y)))
+
+    def _get_YYTfactor(self, Y):
+        """
+        find a matrix L which satisfies LLT = YYT.
+
+        Note that L may have fewer columns than Y.
+        """
+        N, D = Y.shape
+        if (N>=D):
+            return param_to_array(Y)
+        else:
+            return jitchol(tdot(Y))
+        
+    def inference_likelihood(self, kern, X, Z, likelihood, Y):
+        """
+        The first phase of inference:
+        Compute: log-likelihood, dL_dKmm
+        
+        Cached intermediate results: Kmm, KmmInv,
+        """
+        
+        num_inducing = Z.shape[0]        
+        num_data, output_dim = Y.shape
+
+        if isinstance(X, VariationalPosterior):
+            uncertain_inputs = True
+        else:
+            uncertain_inputs = False
+        
+        #see whether we've got a different noise variance for each datum
+        beta = 1./np.fmax(likelihood.variance, 1e-6)
+        het_noise = beta.size > 1
+        # VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency!
+        #self.YYTfactor = beta*self.get_YYTfactor(Y)
+        YYT_factor = Y
+        trYYT = self.get_trYYT(Y)
+        
+        
+        psi2_full = np.zeros((num_inducing,num_inducing))
+        psi1Y_full = np.zeros((output_dim,num_inducing)) # DxM
+        psi0_full = 0
+        YRY_full = 0
+        
+        for n_start in xrange(0,num_data,self.batchsize):
+            
+            n_end = min(self.batchsize+n_start, num_data)
+            
+            Y_slice = YYT_factor[n_start:n_end]
+            X_slice = X[n_start:n_end]
+            
+            if uncertain_inputs:
+                psi0 = kern.psi0(Z, X_slice)
+                psi1 = kern.psi1(Z, X_slice)
+                psi2 = kern.psi2(Z, X_slice)
+            else:
+                psi0 = kern.Kdiag(X_slice)
+                psi1 = kern.K(X_slice, Z)
+                psi2 = None
+                
+            if het_noise:
+                beta_slice = beta[n_start:n_end]
+                psi0_full += (beta_slice*psi0).sum()
+                psi1Y_full += np.dot(beta_slice*Y_slice.T,psi1) # DxM
+                YRY_full += (beta_slice*np.square(Y_slice).sum(axis=-1)).sum()
+            else:
+                psi0_full += psi0.sum()
+                psi1Y_full += np.dot(Y_slice.T,psi1) # DxM
+                
+                
+            if uncertain_inputs:
+                if het_noise:
+                    psi2_full += np.einsum('n,nmo->mo',beta_slice,psi2)
+                else:
+                    psi2_full += psi2.sum(axis=0)
+            else:
+                if het_noise:
+                    psi2_full += np.einsum('n,nm,no->mo',beta_slice,psi1,psi1)
+                else:
+                    psi2_full += tdot(psi1.T)
+                
+        if not het_noise:
+            psi0_full *= beta
+            psi1Y_full *= beta
+            psi2_full *= beta
+            YRY_full = trYYT*beta
+            
+        #======================================================================
+        # Compute Common Components
+        #======================================================================
+        
+        Kmm = kern.K(Z).copy()
+        diag.add(Kmm, self.const_jitter)
+        Lm = jitchol(Kmm)
+                
+        Lambda = Kmm+psi2_full
+        LL = jitchol(Lambda)
+        b,_ = dtrtrs(LL, psi1Y_full.T)
+        bbt = np.square(b).sum()
+        v,_ = dtrtrs(LL.T,b,lower=False)
+        vvt = np.einsum('md,od->mo',v,v)
+        LmInvPsi2LmInvT = backsub_both_sides(Lm,psi2_full,transpose='right')
+        
+        Psi2LLInvT = dtrtrs(LL,psi2_full)[0].T
+        LmInvPsi2LLInvT= dtrtrs(Lm,Psi2LLInvT)[0]
+        KmmInvPsi2LLInvT = dtrtrs(Lm,LmInvPsi2LLInvT,trans=True)[0]
+        KmmInvPsi2P = dtrtrs(LL,KmmInvPsi2LLInvT.T, trans=True)[0].T
+        
+        dL_dpsi2R = (output_dim*KmmInvPsi2P - vvt)/2. # dL_dpsi2 with R inside psi2
+        
+        # Cache intermediate results
+        self.midRes['dL_dpsi2R'] = dL_dpsi2R
+        self.midRes['v'] = v
+                
+        #======================================================================
+        # Compute log-likelihood
+        #======================================================================
+        if het_noise:
+            logL_R = -np.log(beta).sum()
+        else:
+            logL_R = -num_data*np.log(beta)
+        logL = -(output_dim*(num_data*log_2_pi+logL_R+psi0_full-np.trace(LmInvPsi2LmInvT))+YRY_full-bbt)/2.-output_dim*(-np.log(np.diag(Lm)).sum()+np.log(np.diag(LL)).sum())
+
+        #======================================================================
+        # Compute dL_dKmm
+        #======================================================================
+        
+        dL_dKmm =  -(output_dim*np.einsum('md,od->mo',KmmInvPsi2LLInvT,KmmInvPsi2LLInvT) + vvt)/2.
+
+        #======================================================================
+        # Compute the Posterior distribution of inducing points p(u|Y)
+        #======================================================================
+        
+#         phi_u_mean = np.dot(Kmm,v)
+#         LLInvKmm,_ = dtrtrs(LL,Kmm)
+# #        phi_u_var = np.einsum('ma,mb->ab',LLInvKmm,LLInvKmm)
+#         phi_u_var = Kmm - np.dot(LLInvKmm.T,LLInvKmm)
+        
+        post = Posterior(woodbury_inv=KmmInvPsi2P, woodbury_vector=v, K=Kmm, mean=None, cov=None, K_chol=Lm)
+
+        return logL, dL_dKmm, post
+
+    def inference_minibatch(self, kern, X, Z, likelihood, Y):
+        """
+        The second phase of inference: Computing the derivatives over a minibatch of Y 
+        Compute: dL_dpsi0, dL_dpsi1, dL_dpsi2, dL_dthetaL
+        return a flag showing whether it reached the end of Y (isEnd)
+        """
+
+        num_data, output_dim = Y.shape
+
+        if isinstance(X, VariationalPosterior):
+            uncertain_inputs = True
+        else:
+            uncertain_inputs = False
+        
+        #see whether we've got a different noise variance for each datum
+        beta = 1./np.fmax(likelihood.variance, 1e-6)
+        het_noise = beta.size > 1
+        # VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency!
+        #self.YYTfactor = beta*self.get_YYTfactor(Y)
+        YYT_factor = Y
+        
+        n_start = self.batch_pos
+        n_end = min(self.batchsize+n_start, num_data)
+        if n_end==num_data:
+            isEnd = True
+            self.batch_pos = 0
+        else:
+            isEnd = False
+            self.batch_pos = n_end
+        
+        num_slice = n_end-n_start
+        Y_slice = YYT_factor[n_start:n_end]
+        X_slice = X[n_start:n_end]
+        
+        if uncertain_inputs:
+            psi0 = kern.psi0(Z, X_slice)
+            psi1 = kern.psi1(Z, X_slice)
+            psi2 = kern.psi2(Z, X_slice)
+        else:
+            psi0 = kern.Kdiag(X_slice)
+            psi1 = kern.K(X_slice, Z)
+            psi2 = None
+            
+        if het_noise:
+            beta = beta[n_start:n_end]
+
+        betaY = beta*Y_slice
+        betapsi1 = np.einsum('n,nm->nm',beta,psi1)
+        
+        #======================================================================
+        # Load Intermediate Results
+        #======================================================================
+        
+        dL_dpsi2R = self.midRes['dL_dpsi2R']
+        v = self.midRes['v']
+
+        #======================================================================
+        # Compute dL_dpsi
+        #======================================================================
+        
+        dL_dpsi0 = -0.5 * output_dim * (beta * np.ones((n_end-n_start,)))
+        
+        dL_dpsi1 = np.dot(betaY,v.T)
+        
+        if uncertain_inputs:
+            dL_dpsi2 = np.einsum('n,mo->nmo',beta * np.ones((n_end-n_start,)),dL_dpsi2R)
+        else:
+            dL_dpsi1 += np.dot(betapsi1,dL_dpsi2R)*2.
+            dL_dpsi2 = None
+            
+        #======================================================================
+        # Compute dL_dthetaL
+        #======================================================================
+
+        if het_noise:
+            if uncertain_inputs:
+                psiR = np.einsum('mo,nmo->n',dL_dpsi2R,psi2)
+            else:
+                psiR = np.einsum('nm,no,mo->n',psi1,psi1,dL_dpsi2R)
+            
+            dL_dthetaL = ((np.square(betaY)).sum(axis=-1) + np.square(beta)*(output_dim*psi0)-output_dim*beta)/2. - np.square(beta)*psiR- (betaY*np.dot(betapsi1,v)).sum(axis=-1)
+        else:
+            if uncertain_inputs:
+                psiR = np.einsum('mo,nmo->',dL_dpsi2R,psi2)
+            else:
+                psiR = np.einsum('nm,no,mo->',psi1,psi1,dL_dpsi2R)
+            
+            dL_dthetaL = ((np.square(betaY)).sum() + np.square(beta)*output_dim*(psi0.sum())-num_slice*output_dim*beta)/2. - np.square(beta)*psiR- (betaY*np.dot(betapsi1,v)).sum()
+
+        if uncertain_inputs:
+            grad_dict = {'dL_dpsi0':dL_dpsi0,
+                         'dL_dpsi1':dL_dpsi1,
+                         'dL_dpsi2':dL_dpsi2,
+                         'dL_dthetaL':dL_dthetaL}
+        else:
+            grad_dict = {'dL_dKdiag':dL_dpsi0,
+                         'dL_dKnm':dL_dpsi1,
+                         'dL_dthetaL':dL_dthetaL}
+            
+        return isEnd, (n_start,n_end), grad_dict
+    

GPy/models/bayesian_gplvm.py

@@ -8,7 +8,7 @@ from ..core import SparseGP
 from ..likelihoods import Gaussian
 from ..inference.optimization import SCG
 from ..util import linalg
-from ..core.parameterization.variational import NormalPosterior, NormalPrior
+from ..core.parameterization.variational import NormalPosterior, NormalPrior,VariationalPosterior
 
 class BayesianGPLVM(SparseGP):
     """
@@ -62,6 +62,10 @@ class BayesianGPLVM(SparseGP):
         self.init = state.pop()
         SparseGP._setstate(self, state)
 
+    def set_X_gradients(self, X, X_grad):
+        """Set the gradients of the posterior distribution of X in its specific form."""
+        X.mean.gradient, X.variance.gradient = X_grad
+
     def parameters_changed(self):
         super(BayesianGPLVM, self).parameters_changed()
         self._log_marginal_likelihood -= self.variational_prior.KL_divergence(self.X)
@@ -71,7 +75,6 @@ class BayesianGPLVM(SparseGP):
         # update for the KL divergence
         self.variational_prior.update_gradients_KL(self.X)
 
-
     def plot_latent(self, plot_inducing=True, *args, **kwargs):
         """
         See GPy.plotting.matplot_dep.dim_reduction_plots.plot_latent
@@ -150,6 +153,56 @@ class BayesianGPLVM(SparseGP):
         return dim_reduction_plots.plot_steepest_gradient_map(self,*args,**kwargs)
 
 
+def update_gradients(model):
+    model._log_marginal_likelihood, dL_dKmm, model.posterior = model.inference_method.inference_likelihood(model.kern, model.X, model.Z, model.likelihood, model.Y)
+    
+    het_noise = model.likelihood.variance.size > 1
+    
+    if het_noise:
+        dL_dthetaL = np.empty((model.Y.shape[0],))
+    else:
+        dL_dthetaL = 0
+
+    #gradients w.r.t. kernel
+    model.kern.update_gradients_full(dL_dKmm, model.Z, None)
+    kern_grad = model.kern.gradient.copy()
+            
+    #gradients w.r.t. Z
+    model.Z.gradient[:,model.kern.active_dims] = model.kern.gradients_X(dL_dKmm, model.Z)
+    
+    isEnd = False
+    while not isEnd:
+        isEnd, n_range, grad_dict = model.inference_method.inference_minibatch(model.kern, model.X, model.Z, model.likelihood, model.Y)
+        if isinstance(model.X, VariationalPosterior):
+            
+            #gradients w.r.t. kernel
+            model.kern.update_gradients_expectations(variational_posterior=model.X[n_range[0]:n_range[1]], Z=model.Z, dL_dpsi0=grad_dict['dL_dpsi0'], dL_dpsi1=grad_dict['dL_dpsi1'], dL_dpsi2=grad_dict['dL_dpsi2'])
+            kern_grad += model.kern.gradient
+    
+            #gradients w.r.t. Z
+            model.Z.gradient[:,model.kern.active_dims] += model.kern.gradients_Z_expectations(
+                               grad_dict['dL_dpsi1'], grad_dict['dL_dpsi2'], Z=model.Z, variational_posterior=model.X[n_range[0]:n_range[1]])
+        
+            #gradients w.r.t. posterior parameters of X
+            X_grad = model.kern.gradients_qX_expectations(variational_posterior=model.X[n_range[0]:n_range[1]], Z=model.Z, dL_dpsi0=grad_dict['dL_dpsi0'], dL_dpsi1=grad_dict['dL_dpsi1'], dL_dpsi2=grad_dict['dL_dpsi2'])
+            model.set_X_gradients(model.X[n_range[0]:n_range[1]], X_grad)
+                
+            if het_noise:
+                dL_dthetaL[n_range[0]:n_range[1]] = grad_dict['dL_dthetaL']
+            else:
+                dL_dthetaL += grad_dict['dL_dthetaL']
+    
+    # Set the gradients w.r.t. kernel
+    model.kern.gradient = kern_grad
+
+    # Update Log-likelihood
+    model._log_marginal_likelihood -= model.variational_prior.KL_divergence(model.X)
+    # update for the KL divergence
+    model.variational_prior.update_gradients_KL(model.X)
+    
+    # dL_dthetaL
+    model.likelihood.update_gradients(dL_dthetaL)
+
 def latent_cost_and_grad(mu_S, kern, Z, dL_dpsi0, dL_dpsi1, dL_dpsi2):
     """
     objective function for fitting the latent variables for test points