Implementation of mixture distributions (#22742)
Summary:
Addressing issue https://github.com/pytorch/pytorch/issues/18125
This implements a mixture distributions, where all components are from the same distribution family. Right now the implementation supports the ```mean, variance, sample, log_prob``` methods.
cc: fritzo and neerajprad
- [x] add import and `__all__` string in `torch/distributions/__init__.py`
- [x] register docs in docs/source/distributions.rst
### Tests
(all tests live in tests/distributions.py)
- [x] add an `Example(MixtureSameFamily, [...])` to the `EXAMPLES` list,
populating `[...]` with three examples:
one with `Normal`, one with `Categorical`, and one with `MultivariateNormal`
(to exercise, `FloatTensor`, `LongTensor`, and nontrivial `event_dim`)
- [x] add a `test_mixture_same_family_shape()` to `TestDistributions`. It would be good to test this with both `Normal` and `MultivariateNormal`
- [x] add a `test_mixture_same_family_log_prob()` to `TestDistributions`.
- [x] add a `test_mixture_same_family_sample()` to `TestDistributions`.
- [x] add a `test_mixture_same_family_shape()` to `TestDistributionShapes`
### Triaged for follup-up PR?
- support batch shape
- implement `.expand()`
- implement `kl_divergence()` in torch/distributions/kl.py
Pull Request resolved: https://github.com/pytorch/pytorch/pull/22742
Differential Revision: D19899726
Pulled By: ezyang
fbshipit-source-id: 9c816e83a2ef104fe3ea3117c95680b51c7a2fa4
