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I'm dealing with a low event rate problem (e.g. credit card fraud). I've balanced my data with SMOTE, and ran a neural net model (cross validated with recall as the measure).

However my precision (as can be expected) is very low.

I want to use the positive predictions (TP + FP) from my model as an input to another model - a subset of the original data. Creating a sort of "pipeline". Practically speaking, If a credit card company were to use my model, all the positive predictions will be handled by a human who would than decide whether or not it's a fraud, so why not automate?

Just like model stacking, but the stacked model gets a subset of the data and not the previous models predictions.

I'm not sure if that's OK. Any thoughts?

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stacking, is exactly use the prediction of previous models. You can find the ensemble method in the following book:

Z.-H. Zhou. Ensemble Methods: Foundations and Algorithms, Boca Raton, FL: Chapman & Hall/CRC, 2012. (ISBN 978-1-439-830031)

I think you method, just use the TP and FP not very well, except the recall metrics is good enough.

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