Proposition 539 of 39 in the corpus
A number means what the split lets it mean.
The unit of the split has to be the unit the claim is about. Split below that unit and the held-out score measures recall of things already seen, however carefully everything else was done.
Depends on
Demonstration
Take a retinal dataset with several photographs per patient. Split at random by image and each patient’s photographs land on both sides of the boundary. The held-out score is then a measure of how well the model recognises another photograph of an eye it has already seen — which is a real capability, and not the one the paper claims.
The rule generalises: the unit of the split must be at least the unit the claim is about. If the claim is about new patients, split by patient. If it is about new hospitals, split by site. If it is about next month, split by time and put the future on the held-out side.
The failure has a family of relatives, all of which produce optimistic numbers that survive review:
Preprocessing before splitting. Normalisation statistics, feature selection or resampling computed over the whole dataset carry information from the held-out set into training. Fit them on the training split only.
Temporal leakage. Random splits of time series put the future in the training set. Almost any forecasting model looks excellent under this arrangement.
Test-set reuse. Each consultation of the test set to make a decision leaks a little, and the leak accumulates in the flattering direction. Three splits exist for a reason: train to fit, validation to choose, test to report once.
Duplicates. Near-identical records — the same study submitted twice, an image and its crop — straddle the split without any obvious sign.
External validation is what settles it. A model evaluated on data from a site that contributed nothing to training has been asked the question the claim is about. The literature on chest radiograph models is instructive: several systems with strong internal numbers degraded substantially on external cohorts, and the degradation was a property of the evaluation rather than of the models.
Corollary
This is the last proposition of Book I because it constrains all the others. An architecture, a loss, a schedule and a precision policy are all judged by a number, and the number is only worth what the split makes it worth. Establish the split first; everything else is a refinement on top of it.