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I'm Spanish and I don't understand the meaning of "non-held-out". I have tried Google Translator and online dictionaries like Longman but I can't find a suitable translation for this term.

You can find these term using this Google Search, and in articles like this one:

  1. "computing SVD on the non-held-out data" from here.
  2. "The training set consists all the images and annotations containing non-held-out classes while held-out classes are masked as background during the training" from Few-Shot Semantic Segmentation with Prototype Learning.
  3. "A cross-validation procedure is that non held out data (meaning after holding out the test set) is splitted in k folds/sets" from here.

What is non-held-out data and held-out data or classes?

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Held-out simply means "not included" particularly in the sense of:

This part of the data was not included in this specific training run.

Depending on the context of all of these text non-held-out data/classes means the data that actually was included in a particular modeling exercise.

Consider this excerpt from your first example:

For instance, Owen and Perry (2009) show a method for holding out data, computing SVD on the non-held-out data, and selecting k so as to minimize the reconstruction error between the held-out data and its SVD approximation.

It actually means:

For instance, Owen and Perry (2009) show a method for excluding data, computing SVD on the remaining data, and selecting k so as to minimize the reconstruction error between the excluded data and its SVD approximation.

So it simply talks about a particular way of train-test-validation splitting the data.

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