Multilevel Bayesian quadrature

[tskarvone]

In a Nutshell

This RP adds a basic multilevel Bayesian quadrature method that is described in Proposition 1 of https://arxiv.org/pdf/2210.08329.pdf.

Detailed Description

• This is essentially nothing more than a loop that calls bayesquad_from_data a number of times and sums the outputs.
• For now the user is required to input the nodes and function evaluations, but it would be easy to include a version where a number of error tolerances that need to be met are provided instead. In that case the current method should probably be renamed e.g. bayesquad_multileve_from_data.
• Testing seems somewhat difficult. Only input handling and trivial cases where the multilevel method reduces to traditional BQ are tested.

It may be that this should be reviewed only after some or all of #746, #748 and #749 are merged.

Related Issues

na

[mmahsereci]

What about multilevel_bayesquad_from_data as name? It would reflect the paper title.

In terms of tests, you can assert the type of the return objects and the length of the info list.

[tskarvone]

What about multilevel_bayesquad_from_data as name? It would reflect the paper title.

I've renamed the method as you suggest.

[tskarvone]

All the failed checks are about src/probnum/quad/__init__.py::probnum.quad.multilevel_bayesquad_from_data but I do not understand what the problem is.

[mmahsereci]

hey Toni, some more comments, mainly on the tests, but they should be all fast to fix.

The failing test was a doctest due to numerical imprecision. There is a comment on how to fix it. You can check doctests locally by running tox -e py3 -- src/probnum/quad/ in the root directory.

[codecov]

Codecov Report

Merging #750 (c58dc7a) into main (a980df3) will increase coverage by 0.01%.
The diff coverage is 100.00%.

❗ Current head c58dc7a differs from pull request most recent head be1fa10. Consider uploading reports for the commit be1fa10 to get more accurate results

@@            Coverage Diff             @@
##             main     #750      +/-   ##
==========================================
+ Coverage   91.16%   91.17%   +0.01%     
==========================================
  Files         215      215              
  Lines        7977     7993      +16     
  Branches     1015     1019       +4     
==========================================
+ Hits         7272     7288      +16     
  Misses        479      479              
  Partials      226      226              

Impacted Files	Coverage Δ
src/probnum/quad/__init__.py	100.00% <100.00%> (ø)
src/probnum/quad/_bayesquad.py	100.00% <100.00%> (ø)

[tskarvone]

Thank you, Maren. That seems to have fixed most of the checks, though a Jupyter Notebook check still eludes me.

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[mmahsereci]

Thank you, Maren. That seems to have fixed most of the checks, though a Jupyter Notebook check still eludes me.

It doesn't seem to be related to the changes you made but a separate issue.

I made some cosmetic changes. Can you check if you're OK with it?

[mmahsereci]

@JonathanWenger @marvinpfoertner As the jupyter test seems to be failing for other reasons (see #781 ) we'll merge this anyways if it's OK with everyone (once the rest of the tests pass of course.)

[tskarvone]

Thanks again, Maren. Your changes look OK. Happy to have this merged now.

[JonathanWenger]

@JonathanWenger @marvinpfoertner As the jupyter test seems to be failing for other reasons (see #781 ) we'll merge this anyways if it's OK with everyone (once the rest of the tests pass of course.)

I just fixed this, see #783 . But merging this PR first is also fine with me.