title: Classification - modified huber loss: how is it more tolerant to outliers?
body: <p>According to the scikit-learn SGDClassifier <a href="http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.SGDClassifier.html" rel="nofollow noreferrer">documentation</a> , modified Huber loss function can be used to offer higher tolerance to outliers.</p>
  
  <p>Having a look at the <a href="http://scikit-learn.org/stable/auto_examples/linear_model/plot_sgd_loss_functions.html" rel="nofollow noreferrer">plot</a> of the cost function though, doesn't it seem like Modified Huber is <em>less</em> tolerant? It appears to give higher cost to observations with f(x)&lt;0, i.e. to observations that lie on the wrong side of the margin. Isn't this correct?
  <a href="https://i.stack.imgur.com/RUIJ4.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/RUIJ4.png" alt="enter image description here"></a></p>