diff --git a/GPy/core/mapping.py b/GPy/core/mapping.py
index ef0af16c..efd9476f 100644
--- a/GPy/core/mapping.py
+++ b/GPy/core/mapping.py
@@ -10,11 +10,11 @@ class Mapping(Parameterized):
     Base model for shared behavior between models that can act like a mapping.
     """
 
-    def __init__(self, input_dim, output_dim):
+    def __init__(self, input_dim, output_dim, name='mapping'):
         self.input_dim = input_dim
         self.output_dim = output_dim
 
-        super(Mapping, self).__init__()
+        super(Mapping, self).__init__(name=name)
         # Model.__init__(self)
         # All leaf nodes should call self._set_params(self._get_params()) at
         # the end
diff --git a/GPy/mappings/linear.py b/GPy/mappings/linear.py
index 5846903d..075b8556 100644
--- a/GPy/mappings/linear.py
+++ b/GPy/mappings/linear.py
@@ -3,6 +3,7 @@
 
 import numpy as np
 from ..core.mapping import Mapping
+from ..core.parameterization import Param
 
 class Linear(Mapping):
     """
@@ -16,38 +17,22 @@ class Linear(Mapping):
     :type X: ndarray
     :param output_dim: dimension of output.
     :type output_dim: int
-    
+
     """
 
-    def __init__(self, input_dim=1, output_dim=1):
-        self.name = 'linear'
-        Mapping.__init__(self, input_dim=input_dim, output_dim=output_dim)
-        self.num_params = self.output_dim*(self.input_dim + 1)
-        self.W = np.array((self.input_dim, self.output_dim))
-        self.bias = np.array(self.output_dim)
-        self.randomize()
-
-    def _get_param_names(self):
-        return sum([['W_%i_%i' % (n, d) for d in range(self.output_dim)] for n in range(self.input_dim)], []) + ['bias_%i' % d for d in range(self.output_dim)]
-
-    def _get_params(self):
-        return np.hstack((self.W.flatten(), self.bias))
-
-    def _set_params(self, x):
-        self.W = x[:self.input_dim * self.output_dim].reshape(self.input_dim, self.output_dim).copy()
-        self.bias = x[self.input_dim*self.output_dim:].copy()
-    def randomize(self):
-        self.W = np.random.randn(self.input_dim, self.output_dim)/np.sqrt(self.input_dim + 1)
-        self.bias = np.random.randn(self.output_dim)/np.sqrt(self.input_dim + 1)
+    def __init__(self, input_dim=1, output_dim=1, name='linear_map'):
+        Mapping.__init__(self, input_dim=input_dim, output_dim=output_dim, name=name)
+        self.W = Param('W',np.array((self.input_dim, self.output_dim)))
+        self.bias = Param('bias',np.array(self.output_dim))
+        self.add_parameters(self.W, self.bias)
 
     def f(self, X):
         return np.dot(X,self.W) + self.bias
 
     def df_dtheta(self, dL_df, X):
-        self._df_dW = (dL_df[:, :, None]*X[:, None, :]).sum(0).T
-        self._df_dbias = (dL_df.sum(0))
-        return np.hstack((self._df_dW.flatten(), self._df_dbias))
-        
-    def df_dX(self, dL_df, X):
-        return (dL_df[:, None, :]*self.W[None, :, :]).sum(2) 
-    
+        df_dW = (dL_df[:, :, None]*X[:, None, :]).sum(0).T
+        df_dbias = (dL_df.sum(0))
+        return np.hstack((df_dW.flatten(), df_dbias))
+
+    def dL_dX(self, dL_df, X):
+        return (dL_df[:, None, :]*self.W[None, :, :]).sum(2)