Add InnerDirichletPartitioner

[adam-narozniak]

Proposal

Add Inner Dirichlet Partitioner based on Federated Learning Based on Dynamic Regularization https://arxiv.org/abs/2111.04263.

Explanation

This variation of Dirchlet-based partitioning differs from the #2795.

This implementation does the following:

• Originally draws the number of samples - partition sizes - from the lognormal distribution, here it is parameterized by partition_sizes and required to be provided by a user.
• The Dirichlet distribution is used to create the fraction for each partition separately. There, it decided on the division of classes per partition (the probabilities from Dirichlet sum to one per each partition; central to the original Dirichlet where the fractions sum up to 1 along all partitions of class k).

How does it differ from the original Dirichlet from #2795?
This implementation is used to choose to divide classes among partitions. The Dirichlet distribution is drawn such that the class n is split among p partitions. This is repeated N (number of unique classes) times. Therefore, there's no need to decide on the size of each partition in the original Dirichlet.

Also, what might help to understand the difference is to think about the shape of the alpha value (concentration) for the Dirichlet.
Original: size is equal to the number of partitions (and is repeated the number of unique classes)
This implementation: size equals the number of unique classes (and is repeated the number of partitions).

Note that it also means that at a certain point in this implementation, we run out of the samples from class n while sampling for later partitions, and the code needs to be adjusted for that (to give other samples in that case).

[jafermarq]

Some initial comments