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If the test-set RMSE error of a model is less than cross-validated RMSE error, how can I interpret this?

Is this abnormal? Does it imply a mistake in the methodology?

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  • $\begingroup$ It doesn't mean anything. It happens. $\endgroup$ – Aksakal Jan 12 '15 at 23:57
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    $\begingroup$ Did you check confidence intervals on both errors? Are your test and training samples large enough to warrant the conclusion that the test error is lower? $\endgroup$ – cbeleites Jan 13 '15 at 9:33
  • $\begingroup$ Yes, the C.I's are non-overlapping and the test error is lower. Is there something u'd like to infer about this situation? Else, I was planning to accept Aksakal's answer as final..unless there is a different thought put-forth. $\endgroup$ – user75402 Jan 13 '15 at 19:00
  • $\begingroup$ It happens a lot in machine learning. I do not think that it means nothing. I notice a high correlation between this phenomena and poor performance during further out of sample validation where the ground truth is known. It may be a form of overfitting in the case of bagging models, since cross-validation is used to inform the model during training in this case. $\endgroup$ – Hack-R Feb 28 '16 at 20:25
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Like Aksakal said this is something that can happen naturally. As an illustration, imagine a dataset X which is split into pieces X_1 and X_2. Suppose the rmse for a model trained on X_1 but tested on X_2 is 2 and the rmse for a model trained on X_2 but tested on X_1 is 3. Then if we used two fold cross validation (with the above folds) we'd find that the CV error would be 5/2, right? Then suppose, separately and by chance, we chose our training set to be X_1 and our test set to be X_2. We would find that our test error would be 2. Nothing was necessarily wrong with our methodology but we ended up with test rmse less than our CV rmse.

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