Added description, and code for Huber loss. (#39)

modified:   code/loss_functions.py
	modified:   docs/loss_functions.rst

code/loss_functions.py

@@ -27,8 +27,8 @@ def Hinge(yHat, y):
     return np.max(0, 1 - yHat * y)
 
 
-def Huber(yHat, y):
-    pass
+def Huber(yHat, y, delta=1.):
+    return np.where(np.abs(y-yHat) < delta,.5*(y-yHat)**2 , delta*(np.abs(y-yHat)-0.5*delta))
 
 
 def KLDivergence(yHat, y):

docs/loss_functions.rst

@@ -68,13 +68,23 @@ Used for classification.
 Huber
 =====
 
-Typically used for regression. It's less sensitive to outliers than the MSE.
+Typically used for regression. It's less sensitive to outliers than the MSE as it treats error as square only inside an interval.
+
+.. math::
+
+  L_{\delta}=\left\{\begin{matrix}
+  \frac{1}{2}(y - \hat{y})^{2} & if \left | (y - \hat{y})  \right | < \delta\\
+  \delta (y - \hat{y}) - \frac1 2 \delta & otherwise
+  \end{matrix}\right.
 
 .. rubric:: Code
 
 .. literalinclude:: ../code/loss_functions.py
       :pyobject: Huber
 
+Further information can be found at `Huber Loss in Wikipedia`_.  
+
+.. _`Huber Loss in Wikipedia`: https://en.wikipedia.org/wiki/Huber_loss
 
 .. _kl_divergence: