Add support for CorrCholeskyTransform (#48041)
Summary:
This adds a transform to convert a real vector of (D * (D-1))/2 dimension into the cholesky factor of a D x D correlation matrix. This follows the implementation in [NumPyro](https://github.com/pyro-ppl/numpyro/blob/master/numpyro/distributions/transforms.py) by fehiepsi. This is needed for the LKJDistribution which will be added in a subsequent PR.
Also in line with the ongoing effort to refactor distributions test, this moves the transforms test into its own file that uses pytest with parametrized fixtures.
For review:
fehiepsi - could you help review the math?
fritzo - do you have any suggestions for what to do about the event dimension (more details are in the comment below)?
ezyang - could you review the changes in `run_test.py`? Instead of a separate `PYTEST_TESTS`, I have clubbed these tests in `USE_PYTEST_LIST` to avoid duplicate logic. The only difference is that we do not anymore check if pytest is not installed and exclude the tests in the list. I figured that if existing tests are already using pytest, this should not matter.
TODOs (probably not all can be satisfied at the same time):
- [x] Use operations that are JIT friendly, i.e. the transform works with different sized input under JIT.
- [x] Resolve test failures - currently `arange(scalar_tensor)` fails on certain backends but this is needed for JIT. Maybe we should only support same sized tensor under JIT?
- [x] Add tests to check that the transform gives correct gradients and is in agreement with the `log_det_jacobian`.
- [x] Add `input_event_dim` and `output_event_dim` to `CorrCholeskyTransform`.
Pull Request resolved: https://github.com/pytorch/pytorch/pull/48041
Reviewed By: zhangguanheng66
Differential Revision: D25262505
Pulled By: neerajprad
fbshipit-source-id: 5a57e1c19d8230b53592437590b9169bdf2f71e9