In general, what efficiency is expected from neural networks when the input is irrelevant data? Is it expected to lie around 50%?
Less than this? More?
"Irrelevant data" could be anything not related to the targets. For example, it could be random data, or it could be a dataset from problem A paired up with targets taken from an unrelated problem B, etc.
I imagine that the inverse question would be equivalent to this one - for which efficiency should I start suspecting that my data are meaningless?
Edit: Let's assume a random rate of success around 50% (or anything you may like to define). I think my concern boils down to whether we expect a 50% from the NN, or whether there are known "fake effects". I imagine that overfitting would be one such contribution (edit: but only for the training test).
 A: You mean train set, or test set performance? On train set this can be anything up to 100% accuracy. On test set, if you have no data leaks, it cannot be anything better than what you got from random guessing. Of course, this assumes that “irrelevant” labels are random and give really no information. If the labels are just noisy, but have some informational value, the result would depend on many things, like data quality, or using appropriate model for this kind of data, etc.
A: Your last question is more sound because no algorithm can be truly successful on irrelevant data. To judge if your data is meaningless or not you can use random data instead of your features, or permute your features to break the correlations. Then, you can compare resulting performances with your original results.
A: If your output is binary (for example, a 0 or 1 classification), then an accuracy around 50% is meaningless because, since you have two outputs, a correct classification of 50% is merely random.
If your output is not binary, a good accuracy really depends on what is the meaning of your output and what you expect to achieve with it.
To check if your data is meaningless, an useful method would be to perform permutations - if your accuracy with permutations is similar to the accuracy of your dataset, then your data is probably meaningless/random. If the accuracy decreases a lot, then your data is probably fine and you just need to decide if that 50% accuracy you obtained is suitable for your purpose!
You could also perform a PLS on your data - it allows you to check the variables that are contributing more and less to the model, and if they have a positive or negative correlation with the output (if the correlations are all close to zero, then there is probably no logical correlation between your variables and the output).
