From 1a59d527a3327847918099880ef2b30f70b15ca5 Mon Sep 17 00:00:00 2001
From: Zhenwen Dai <z.dai@sheffield.ac.uk>
Date: Mon, 13 Oct 2014 18:00:11 +0100
Subject: [PATCH] generalize the inference of X framework and with support of
 missing data

---
 .../latent_function_inference/inference_X.py  | 91 +++++++++++++++++++
 1 file changed, 91 insertions(+)
 create mode 100644 GPy/inference/latent_function_inference/inference_X.py

diff --git a/GPy/inference/latent_function_inference/inference_X.py b/GPy/inference/latent_function_inference/inference_X.py
new file mode 100644
index 00000000..c28731c3
--- /dev/null
+++ b/GPy/inference/latent_function_inference/inference_X.py
@@ -0,0 +1,91 @@
+"""
+"""
+import numpy as np
+from ...core import Model
+from ...core.parameterization import variational
+
+def inference_newX(model, Y_new, optimize=True):
+    infr_m = Inference_X(model, Y_new)
+    
+    if optimize:
+        infr_m.optimize()
+        
+    return infr_m.X, infr_m
+
+class Inference_X(Model):
+    """The class for inference of new X with given new Y. (do_test_latent)"""
+    def __init__(self, model, Y, name='inference_X'):
+        """TODO: give comments"""
+        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(Inference_X, self).__init__(name)
+        self.likelihood = model.likelihood.copy()
+        self.kern = model.kern.copy()
+        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)
+        self.compute_dL()
+        
+        self.link_parameter(self.X)
+    
+    def _init_X(self, model, Y_new):
+        # 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]
+            l2 = -2.*Y_new.dot(Y.T) + np.square(Y_new).sum(axis=1)[:,None]+ np.square(Y).sum(axis=1)[None,:]
+        else:
+            l2 = -2.*Y_new.dot(Y.T) + np.square(Y_new).sum(axis=1)[:,None]+ np.square(Y).sum(axis=1)[None,:]
+        idx = l2.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[:,i].tie_together() for i in xrange(X.gamma.shape[1])] # Tie columns together
+        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)
+        
+        self._log_marginal_likelihood -= self.variational_prior.KL_divergence(self.X)
+        self.variational_prior.update_gradients_KL(self.X)
+        
+    def log_likelihood(self):
+        return self._log_marginal_likelihood
+