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When a dataset is given and it is divided into N parts, training a Cart on N-1 parts and testing it on the remaining part (and doing that N times, i.e. for each possible leave-out), one ends up with N (different) Carts. So there is not only one model tested, but N different ones, isn't it? Does that make sense?

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    $\begingroup$ Can you clarify your actual question? Yes, there are N different models, but I suspect that isn't what you really want to know. $\endgroup$ Commented Jul 4, 2015 at 0:30
  • $\begingroup$ Isn't cross validation a method for validating a single model. Here, there are N models (unless a model is defined as any Cart tree of a given depth e.g. 3). But how do you assess a model if there are in fact N different models (so, which of the N Cart trees is to be selected)? $\endgroup$ Commented Jul 5, 2015 at 13:37

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since I couldn't reply to your comment. I wrote in an answer.

1) The purpose of cross-validation in cart is to choose the proper complexity parameter. So to serve this purpose, the N models in cart is for calculating complexity parameter (cp) values' cross validation(c-v) error. And then chose the value for cp with the lowest c-v error.

2) As the purpose of c-v is not only evaluating a single model, but also to evaluate complexity parameter value.

All in all, using N-folder makes sense.

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