Maybe we should add a note that this is equivalent  to variance reduction?
Still have not found the time for your thesis :-/


On 07/09/2015 03:30 PM, Sebastian Raschka wrote:
> Thanks, I think my confusion came from the fact that they use x_i as target 
> variable, and I was thinking of feature/attribute when I saw the equation; 
> makes sense now!
>
> Btw. That's a beautiful thesis and a useful reference, too!
>
> Best,
> Sebastian
>
>> On Jul 9, 2015, at 2:23 PM, Gilles Louppe <g.lou...@gmail.com> wrote:
>>
>> Hi Sebastian,
>>
>> Both terminology are in fact strictly equivalent for regression. See
>> e.g. page 46 of http://arxiv.org/abs/1407.7502
>>
>> Best,
>> Gilles
>>
>> On 9 July 2015 at 18:56, Sebastian Raschka <se.rasc...@gmail.com> wrote:
>>> Hi, all,
>>>
>>> sorry, but I have another question regarding the terminology in the 
>>> documentation.
>>>
>>> In the DecisionTreeRegressor's documentation at
>>> http://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeRegressor.html#sklearn.tree.DecisionTreeRegressor
>>> is says
>>>
>>> criterion : string, optional (default=”mse”)
>>> The function to measure the quality of a split. The only supported 
>>> criterion is “mse” for the mean squared error.
>>>
>>> However, I am wondering if the impurity measure is truly the MSE or if it 
>>> is the variance of the nodes (since the wikipedia link on that page refers 
>>> to the "variance reduction" algorithm)? Here, I think of MSE as the average 
>>> of squared deviations of the predictions from the true values, whereas 
>>> variance would be the average of squared deviation of the observations from 
>>> the sample mean of a node.
>>>
>>> Best,
>>> Sebastian
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