add new inference X

GPy/core/parameterization/variational.py

@@ -94,6 +94,9 @@ class VariationalPosterior(Parameterized):
         if self.has_uncertain_inputs():
             assert self.variance.shape == self.mean.shape, "need one variance per sample and dimenion"
 
+    def set_gradients(self, grad):
+        self.mean.gradient, self.variance.gradient = grad
+
     def _raveled_index(self):
         index = np.empty(dtype=int, shape=0)
         size = 0
@@ -158,6 +161,9 @@ class SpikeAndSlabPosterior(VariationalPosterior):
         self.gamma = Param("binary_prob",binary_prob, Logistic(1e-10,1.-1e-10))
         self.link_parameter(self.gamma)
 
+    def set_gradients(self, grad):
+        self.mean.gradient, self.variance.gradient, self.gamma.gradient = grad
+
     def __getitem__(self, s):
         if isinstance(s, (int, slice, tuple, list, np.ndarray)):
             import copy

GPy/inference/latent_function_inference/inferenceX.py

@@ -0,0 +1,127 @@
+"""
+"""
+import numpy as np
+from ...core import Model
+from ...core.parameterization import variational
+
+def infer_newX(model, Y_new, optimize=True, init='L2'):
+    """
+    Infer the distribution of X for the new observed data *Y_new*.
+    
+    :param model: the GPy model used in inference
+    :type model: GPy.core.Model
+    :param Y_new: the new observed data for inference
+    :type Y_new: numpy.ndarray
+    :param optimize: whether to optimize the location of new X (True by default)
+    :type optimize: boolean
+    :return: a tuple containing the estimated posterior distribution of X and the model that optimize X 
+    :rtype: (GPy.core.parameterization.variational.VariationalPosterior, GPy.core.Model)
+    """
+    infr_m = InferenceX(model, Y_new, init=init)
+    
+    if optimize:
+        infr_m.optimize()
+        
+    return infr_m.X, infr_m
+
+class InferenceX(Model):
+    """
+    The class for inference of new X with given new Y. (do_test_latent)
+    
+    :param model: the GPy model used in inference
+    :type model: GPy.core.Model
+    :param Y: the new observed data for inference
+    :type Y: numpy.ndarray
+    """
+    def __init__(self, model, Y, name='inferenceX', init='L2'):
+        if np.isnan(Y).any():
+            assert Y.shape[0]==1, "The current implementation of inference X only support one data point at a time with missing data!"
+            self.missing_data = True
+            self.valid_dim = np.logical_not(np.isnan(Y[0]))
+        else:
+            self.missing_data = False
+        super(InferenceX, self).__init__(name)
+        self.likelihood = model.likelihood.copy()
+        self.kern = model.kern.copy()
+        if model.kern.useGPU:
+            from ...models import SSGPLVM
+            if isinstance(model, SSGPLVM):
+                self.kern.GPU_SSRBF(True)
+            else:
+                self.kern.GPU(True)
+        from copy import deepcopy
+        self.posterior = deepcopy(model.posterior)
+        self.variational_prior = model.variational_prior.copy()
+        self.Z = model.Z.copy()
+        self.Y = Y
+        self.X = self._init_X(model, Y, init=init)
+        self.compute_dL()
+        
+        self.link_parameter(self.X)
+    
+    def _init_X(self, model, Y_new, init='L2'):
+        # Initialize the new X by finding the nearest point in Y space.
+        
+        Y = model.Y
+        if self.missing_data:
+            Y = Y[:,self.valid_dim]
+            Y_new = Y_new[:,self.valid_dim]
+            dist = -2.*Y_new.dot(Y.T) + np.square(Y_new).sum(axis=1)[:,None]+ np.square(Y).sum(axis=1)[None,:]
+        else:
+            if init=='L2':
+                dist = -2.*Y_new.dot(Y.T) + np.square(Y_new).sum(axis=1)[:,None]+ np.square(Y).sum(axis=1)[None,:]
+            elif init=='NCC':
+                dist = Y_new.dot(Y.T)
+        idx = dist.argmin(axis=1)
+        
+        from ...models import SSGPLVM
+        from ...util.misc import param_to_array
+        if isinstance(model, SSGPLVM):
+            X = variational.SpikeAndSlabPosterior(param_to_array(model.X.mean[idx]), param_to_array(model.X.variance[idx]), param_to_array(model.X.gamma[idx]))
+            if model.group_spike:
+                X.gamma.fix()
+        else:
+            X = variational.NormalPosterior(param_to_array(model.X.mean[idx]), param_to_array(model.X.variance[idx]))
+        
+        return X
+        
+    def compute_dL(self):
+        # Common computation
+        beta = 1./np.fmax(self.likelihood.variance, 1e-6)
+        output_dim = self.Y.shape[-1]
+        wv = self.posterior.woodbury_vector
+        if self.missing_data:
+            wv = wv[:,self.valid_dim]
+            output_dim = self.valid_dim.sum()
+            self.dL_dpsi2 = beta*(output_dim*self.posterior.woodbury_inv - np.einsum('md,od->mo',wv, wv))/2.
+            self.dL_dpsi1 = beta*np.dot(self.Y[:,self.valid_dim], wv.T)
+            self.dL_dpsi0 = -output_dim * beta/2.* np.ones(self.Y.shape[0])
+        else:
+            self.dL_dpsi2 = beta*(output_dim*self.posterior.woodbury_inv - np.einsum('md,od->mo',wv, wv))/2.
+            self.dL_dpsi1 = beta*np.dot(self.Y, wv.T)
+            self.dL_dpsi0 = -output_dim * beta/2.* np.ones(self.Y.shape[0])
+                
+    def parameters_changed(self):
+        psi0 = self.kern.psi0(self.Z, self.X)
+        psi1 = self.kern.psi1(self.Z, self.X)
+        psi2 = self.kern.psi2(self.Z, self.X)
+
+        self._log_marginal_likelihood = (self.dL_dpsi2*psi2).sum()+(self.dL_dpsi1*psi1).sum()+(self.dL_dpsi0*psi0).sum()
+        X_grad = self.kern.gradients_qX_expectations(variational_posterior=self.X, Z=self.Z, dL_dpsi0=self.dL_dpsi0, dL_dpsi1=self.dL_dpsi1, dL_dpsi2=self.dL_dpsi2)
+        self.X.set_gradients(X_grad)
+        
+        from ...core.parameterization.variational import SpikeAndSlabPrior
+        if isinstance(self.variational_prior, SpikeAndSlabPrior):
+            # Update Log-likelihood
+            KL_div = self.variational_prior.KL_divergence(self.X, N=self.Y.shape[0])
+            # update for the KL divergence
+            self.variational_prior.update_gradients_KL(self.X, N=self.Y.shape[0])
+        else:
+            # Update Log-likelihood
+            KL_div = self.variational_prior.KL_divergence(self.X)
+            # update for the KL divergence
+            self.variational_prior.update_gradients_KL(self.X)
+        
+    def log_likelihood(self):
+        return self._log_marginal_likelihood
+

GPy/models/bayesian_gplvm.py

@@ -175,6 +175,22 @@ class BayesianGPLVM(SparseGP_MPI):
                 resolution, ax, marker, s,
                 fignum, plot_inducing, legend,
                 plot_limits, aspect, updates, predict_kwargs, imshow_kwargs)
+        
+    def infer_newX(self, Y_new, optimize=True, ):
+        """
+        Infer the distribution of X for the new observed data *Y_new*.
+        
+        :param model: the GPy model used in inference
+        :type model: GPy.core.Model
+        :param Y_new: the new observed data for inference
+        :type Y_new: numpy.ndarray
+        :param optimize: whether to optimize the location of new X (True by default)
+        :type optimize: boolean
+        :return: a tuple containing the estimated posterior distribution of X and the model that optimize X 
+        :rtype: (GPy.core.parameterization.variational.VariationalPosterior, GPy.core.Model)
+        """
+        from ..inference.latent_function_inference.inferenceX import infer_newX
+        return infer_newX(self, Y_new, optimize=optimize)
 
     def do_test_latents(self, Y):
         """