add HSIC metric

[kzkadc]

Description: added Hilbert-Schmidt Independence Criterion (HSIC).

HSIC is a kernel-based method to measure the statistical independence between two feature vectors:

https://papers.nips.cc/paper_files/paper/2007/hash/d5cfead94f5350c12c322b5b664544c1-Abstract.html
https://jejjohnson.github.io/research_journal/appendix/similarity/hsic/

This metric computes the unbiased estimator of the HSIC proposed in the following:

https://jmlr.csail.mit.edu/papers/v13/song12a.html

Check list:

• New tests are added (if a new feature is added)
• New doc strings: description and/or example code are in RST format
• Documentation is updated (if required)

[vfdev-5]

Thanks a lot for the PR @kzkadc !
I have few questions and comments to address.

Please also check failing CI jobs with code formatting issues.

[kzkadc]

@vfdev-5
Are there still problems with this PR?
If so, could you please let me know how I can resolve them?

[vfdev-5]

@kzkadc please check mypy failure:

+ mypy --config-file mypy.ini
ignite/metrics/hsic.py:139: error: Incompatible types in assignment (expression
has type "float", variable has type "Tensor")  [assignment]
                vx = self.sigma_x**2
                     ^~~~~~~~~~~~~~~
ignite/metrics/hsic.py:148: error: Incompatible types in assignment (expression
has type "float", variable has type "Tensor")  [assignment]
                vy = self.sigma_y**2
                     ^~~~~~~~~~~~~~~
Found 2 errors in 1 file (checked 146 source files)

[vfdev-5]

@kzkadc some distributed tests are failing:

=========================== short test summary info ============================
FAILED tests/ignite/metrics/test_hsic.py::TestDistributed::test_integration[gloo_cpu--1.0-1.0] - assert 3.780633494340978e-05 ± 2.0e-05 == 2.1274586519148087e-31
  
  comparison failed
  Obtained: 2.1274586519148087e-31
  Expected: 3.780633494340978e-05 ± 2.0e-05
FAILED tests/ignite/metrics/test_hsic.py::TestDistributed::test_integration[gloo_cpu-1.0--1.0] - assert 3.780633494340978e-05 ± 2.0e-05 == 5.500369049116216e-11
  
  comparison failed
  Obtained: 5.500369049116216e-11
  Expected: 3.780633494340978e-05 ± 2.0e-05
FAILED tests/ignite/metrics/test_hsic.py::TestDistributed::test_integration[gloo_cpu-1.0-1.0] - assert 3.780633494340978e-05 ± 2.0e-05 == 3.3436754842126586e-39
  
  comparison failed
  Obtained: 3.3436754842126586e-39
  Expected: 3.780633494340978e-05 ± 2.0e-05
========== 3 failed, 2 skipped, 3133 deselected, 2 warnings in 7.72s ===========

I haven't checked in details why, but from the first glance something looks weird in the output values which are almost zeros and expected is just close to zero. Any ideas why this happens?

[kzkadc]

I'm struggling with the numerical errors and have been checking the code, but I'm not sure why it happens for now.
I will continue to check the code.

[vfdev-5]

Thanks for the PR @kzkadc !
Approving it, currently the failing job is unrelated, PR is good to go once other CI jobs are green.

[kzkadc]

@vfdev-5 Thank you for fixing the test!