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Currently I'm looking into possibilities to prove that a trained neural network (based on a regression task) performs well on the whole sample space based on statements made from test set metrics. In other words, I want to make sure that there is no sample or region of samples out there, where the network performs badly on, assuming that the sample space is finite.
Are there any well established approaches for this?
A definitive and deterministic answer regarding the existence of adversarial samples is only possible by checking the entire sample space, which you said is finite and hence feasible but maybe too computationally expensive.
I would suggest to generate a grid of samples over the entire space to get a somewhat representative subspace and evaluating the model on it. As you suggested, the normal error distribution out of that whould give you a more or less reliable probabilistic statement on future model errors, depending on the size of the subspace I guess.
However, I also am curious if there is a better way to evaluate ones model reliability.
The easiest way to check whether a neural network performs well or not is by going through an explainable approach.
This library : https://github.com/datamllab/xdeep
Will easily show where exactly your neural network is looking at with barely any added compute power or time. The process also requires very few lines of code!
For more details look into Explainable AI!
An example image of birds is given below:
