API: RandomState deprecation

np.random.RandomState is not a good choice for random number generation going forward:

RandomState is effectively frozen and will only receive updates that are required by changes in the the internals of Numpy. More substantial changes, including algorithmic improvements, are reserved for Generator.

I don’t understand all the details, but the TL;DR I’ve gathered from monitoring some SciPy discussions is that it’s not as good as the new default_rng / Generator-based way of making random numbers and it should be replaced in people’s code.

In the long term I think we want to switch random_state=0 to use default_rng(random_state) instead of RandomState(random_state) internally. I propose:

1. Have a mne.set_rng_backend(backend) that can be 'RandomState' or 'Generator', maybe with a use_rng_backend context manager. The context manager is maybe overkill, but I do think it might help people transition code from old to new, and it’s only a few lines for us.
2. If this has not been called by the user yet, if they do random_state=<int> they will see a DeprecationWarning stating that the default is 'RandomState' in 0.23 but will change to 'Generator' in 0.24 (or maybe this is a good case for making it 0.25 to give people more time to change over), and we will call set_rng_backend('RandomState').
3. In 0.24 (or 0.25) we no longer emit this warning and just use 'Generator'.

I think this is a workable solution for modernizing our random_state params.

[rkern]

Hi everyone! I’m the cause of everyone’s problems here. As you work through these issues, I do recommend reading NEP 19 which goes into more detail about why we had the old backwards-compatibility policy and why we moved away from it. The concerns you have brought up here were definitely in our thoughts. I’m happy to answer any questions that the NEP doesn’t answer.

I can’t speak definitively as to when/how/if scipy really deprecates RandomState per se, but I have my guess as to where we’re going on the aforementioned PR. Some time after we drop support for numpy 1.16, I expect that we will transition the code to use Generator instead of RandomState. I expect that we’ll still accept RandomState instances, but we will wrap its core uniform PRNG in Generator and call its methods instead. So if you call scipy.stats.norm.rvs(random_state=RandomState(1234)), you will get the results from Generator.standard_normal()'s improved algorithm rather than the older, slower RandomState.standard_normal(). The core Mersenne Twister PRNG underneath the passed RandomState will still be used, however. Again, we haven’t made any decisions, yet, but I think that’s where we are going.

[rkern]

Sounds like a good plan.