Add oversampling strategies to interleave datasets
State: closed

Hello everyone,
Here is a proposal to improve `interleave_datasets` function.
Following Issue #3064, and @lhoestq [comment](https://github.com/huggingface/datasets/issues/3064#issuecomment-1022333385), I propose here a code that performs oversampling when interleaving a `Dataset` list. 

I have myself encountered this problem while trying to implement training on a multilingual dataset following a training strategy similar to that of [XLSUM paper](https://arxiv.org/pdf/2106.13822.pdf), a multilingual abstract summary dataset where the multilingual training dataset is created by sampling from the languages following a smoothing strategy. The main idea is to sample  languages that have a low number of samples more frequently than other languages.

As in Issue #3064, the current default strategy is a undersampling strategy, which stops as soon as a dataset runs out of samples. The new `all_exhausted` strategy stops building the new dataset as soon as all samples in each dataset have been added at least once. 

How does it work in practice:
- if ``probabilities`` is `None` and the strategy is `all_exhausted`, it simply performs a round robin interleaving that stops when the longest dataset is out of samples. Here the new dataset length will be $maxLengthDataset*nbDataset$.
- if ``probabilities`` is not `None` and the strategy is `all_exhausted`, it keeps trace of the datasets which were out of samples but continues to add them to the new dataset, and stops as soons as every dataset runs out of samples at least once.
- In the other cases, it is supposed to keep the same behaviour as before. Except that this time, when probabilities are precised, it really stops AS SOON AS a dataset is out of samples.  

More on the last sentence:
The previous example of `interleave_datasets` was:

        >>> from datasets import Dataset, interleave_datasets
        >>> d1 = Dataset.from_dict({"a": [0, 1, 2]})
        >>> d2 = Dataset.from_dict({"a": [10, 11, 12]})
        >>> d3 = Dataset.from_dict({"a": [20, 21, 22]})
        >>> dataset = interleave_datasets([d1, d2, d3])
        >>> dataset["a"]
        [0, 10, 20, 1, 11, 21, 2, 12, 22]
        >>> dataset = interleave_datasets([d1, d2, d3], probabilities=[0.7, 0.2, 0.1], seed=42)
        >>> dataset["a"]
        [10, 0, 11, 1, 2, 20, 12]

With my implementation, `dataset = interleave_datasets([d1, d2, d3], probabilities=[0.7, 0.2, 0.1], seed=42)` gives:
        >>> dataset["a"]
        [10, 0, 11, 1, 2]
because `d1` is already out of samples just after `2` is added.

 Example of the results of applying the different strategies:

        >>> from datasets import Dataset, interleave_datasets
        >>> d1 = Dataset.from_dict({"a": [0, 1, 2]})
        >>> d2 = Dataset.from_dict({"a": [10, 11, 12]})
        >>> d3 = Dataset.from_dict({"a": [20, 21, 22]})
        >>> dataset = interleave_datasets([d1, d2, d3], probabilities=[0.7, 0.2, 0.1], seed=42, stopping_strategy="all_exhausted")
        >>> dataset["a"]
        [10, 0, 11, 1, 2, 20, 12, 10, 0, 1, 2, 21, 0, 11, 1, 2, 0, 1, 12, 2, 10, 0, 22]
        >>> dataset = interleave_datasets([d1, d2, d3], probabilities=[0.7, 0.2, 0.1], seed=42)
        >>> dataset["a"]
        [10, 0, 11, 1, 2]
        >>> dataset = interleave_datasets([d1, d2, d3])
        >>> dataset["a"]
        [0, 10, 20, 1, 11, 21, 2, 12, 22]
        >>> dataset = interleave_datasets([d1, d2, d3], stopping_strategy="all_exhausted")
        >>> dataset["a"]
        [0, 10, 20, 1, 11, 21, 2, 12, 22]
        >>> d1 = Dataset.from_dict({"a": [0, 1, 2]})
        >>> d2 = Dataset.from_dict({"a": [10, 11, 12, 13]})
        >>> d3 = Dataset.from_dict({"a": [20, 21, 22, 23, 24]})
        >>> dataset = interleave_datasets([d1, d2, d3])
        >>> dataset["a"]
        [0, 10, 20, 1, 11, 21, 2, 12, 22]
        >>> dataset = interleave_datasets([d1, d2, d3], stopping_strategy="all_exhausted")
        >>> dataset["a"]
        [0, 10, 20, 1, 11, 21, 2, 12, 22, 0, 13, 23, 1, 0, 24]
        >>> dataset = interleave_datasets([d1, d2, d3], probabilities=[0.7, 0.2, 0.1], seed=42)
        >>> dataset["a"]
        [10, 0, 11, 1, 2]
        >>> dataset = interleave_datasets([d1, d2, d3], probabilities=[0.7, 0.2, 0.1], seed=42, stopping_strategy="all_exhausted")
        >>> dataset["a"]
        [10, 0, 11, 1, 2, 20, 12, 13, ..., 0, 1, 2, 0, 24]

**Final note:** I've been using that code for a research project involving a large-scale multilingual dataset. One should be careful when using oversampling to avoid to avoid exploding the size of the dataset. For example, if a very large data set has a low probability of being sampled, the final dataset may be several times the size of that large data set.