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Has anybody tested how robust a neural network is on random reorderings of the training set? Training a neural net with identical hyperparameters on the same training dataset with random permutations of the datapoints and I observe significant changes in the output. This is valid to a lesser extent for extreme gradient boosting and logistic regression.

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If trained as a model for independent data (that is, the model do not include any components modeling dependence between subjects), then this would not have anything to do with the model itself, but with the training/estimation algorithms. If the algorithm give very different answers under permuting the order of the subjects, then you need a better algorithm. If you want a more specific answer, you should augment the question with detail of the algorithm and implementation used!

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