HSGP improvements

[AlexAndorra]

Closes #7240

Working on this in concert with @bwengals for this example

• Fix the bug in the computation of L
• Do mean-centering of X values under the hood, instead of requiring it from users
• Enable setting prior_linearized with m and c instead of only m and L
• parametrization is not documented
• Add option to pass in nicely named coords to HSGP for the beta coefficients
• Make ._m_star more accessible / user friendly (make a property with no leading underscore so existing code doesn't break), document it, and fix example in prior_linearized docstring.
• Get rid of numpy option, tl=np. It's subtly wrong when calculating the eigen stuff and its not used anywhere.
• Add the approx_params function to hsgp_approx file

Type of change

• New feature / enhancement
• Bug fix

---

📚 Documentation preview 📚: https://pymc--7335.org.readthedocs.build/en/7335/

[AlexAndorra]

The failing test on Windows isn't related to these changes 🤷‍♂️
All the tests are passing

[juanitorduz]

This looks great! Just some minor suggestions :)

Maybe I missed but I missed, but is there a test where we verify the mean sustraction works as expected in the out-of-sample case?

[juanitorduz]

Just a suggestion: what about returning a namedtuple so that we do not depend on the special order of the parameters? something like

HSGPParam = namedtuple('HSGPParam ', ['m', 'c', 'S'])

[AlexAndorra]

Good idea. Done

[bwengals]

Personally think this is over-engineering, because introducing a new HSGPParam type serves no purpose other than to compensate for a perceived defect with the Python language. I think it was clearer before.

[juanitorduz]

No strong opinion here. I just mess up indices so often that I prefer going safe with names instead 🙈

[bwengals]

yah but I would just expect people to unpack like, m, c, S = ....

Which makes me think it might make sense (in this or a later PR) to slightly refactor this so that there's a different function,

S = calc_X_radius(X) # or calc_halfwidth or something

that could be used later where _X_mean was replaced. Then this function only needs to return m and c and not also S, since that's handled now.

[AlexAndorra]

Thanks @juanitorduz ! I just pushed all the changes.

is there a test where we verify the mean sustraction works as expected in the out-of-sample case?

Good point. Added it

[codecov]

Codecov Report

Attention: Patch coverage is 73.68421% with 15 lines in your changes missing coverage. Please review.

Project coverage is 92.37%. Comparing base (fd11cf0) to head (3ca2c2b).
Report is 152 commits behind head on main.

Files with missing lines	Patch %	Lines
pymc/gp/hsgp_approx.py	73.68%	15 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #7335      +/-   ##
==========================================
- Coverage   92.49%   92.37%   -0.13%     
==========================================
  Files         102      102              
  Lines       17173    17208      +35     
==========================================
+ Hits        15885    15896      +11     
- Misses       1288     1312      +24     

Files with missing lines	Coverage Δ
pymc/gp/hsgp_approx.py	88.52% <73.68%> (-7.08%)	⬇️

... and 25 files with indirect coverage changes

[juanitorduz]

Looks great! Just left a comment just to make sure its intentional and not a typo ;)

[bwengals]

Looks like there's one failing test mentioning _X_mean,

         assert np.allclose(
            gp._X_mean, original_mean
>       ), "gp._X_mean should not change after updating data for out-of-sample predictions."
E       AttributeError: 'HSGP' object has no attribute '_X_mean'