diff --git a/GPy/core/gp.py b/GPy/core/gp.py
index f3d1697d..d265161c 100644
--- a/GPy/core/gp.py
+++ b/GPy/core/gp.py
@@ -117,8 +117,10 @@ class GP(Model):
         #         K_{xx} - K_{xp}W_{pp}^{-1}K_{px}
         #         W_{pp} := \texttt{Woodbury inv}
         #         p := _predictive_variable
-        self._predictive_variable = self.X
 
+    @property
+    def _predictive_variable(self):
+        return self.X
 
     def set_XY(self, X=None, Y=None):
         """
@@ -154,7 +156,6 @@ class GP(Model):
                     self.link_parameter(self.X)
             else:
                 self.X = ObsAr(X)
-            self._predictive_variable = self.X
         self.update_model(True)
 
     def set_X(self,X):
diff --git a/GPy/core/sparse_gp.py b/GPy/core/sparse_gp.py
index 9d2d6068..d03ebd5a 100644
--- a/GPy/core/sparse_gp.py
+++ b/GPy/core/sparse_gp.py
@@ -59,8 +59,10 @@ class SparseGP(GP):
         logger.info("Adding Z as parameter")
         self.link_parameter(self.Z, index=0)
         self.posterior = None
-        self._predictive_variable = self.Z
 
+    @property
+    def _predictive_variable(self):
+        return self.Z
 
     def has_uncertain_inputs(self):
         return isinstance(self.X, VariationalPosterior)
diff --git a/GPy/models/gplvm.py b/GPy/models/gplvm.py
index 17d42e5a..5bef5be5 100644
--- a/GPy/models/gplvm.py
+++ b/GPy/models/gplvm.py
@@ -39,7 +39,6 @@ class GPLVM(GP):
 
         self.X = Param('latent_mean', X)
         self.link_parameter(self.X, index=0)
-        self._predictive_variable = self.X
 
     def parameters_changed(self):
         super(GPLVM, self).parameters_changed()
diff --git a/GPy/models/sparse_gp_minibatch.py b/GPy/models/sparse_gp_minibatch.py
index afb8be8c..adb92b30 100644
--- a/GPy/models/sparse_gp_minibatch.py
+++ b/GPy/models/sparse_gp_minibatch.py
@@ -76,7 +76,6 @@ class SparseGPMiniBatch(SparseGP):
         logger.info("Adding Z as parameter")
         self.link_parameter(self.Z, index=0)
         self.posterior = None
-        self._predictive_variable = self.Z
 
     def has_uncertain_inputs(self):
         return isinstance(self.X, VariationalPosterior)