[ENH] Distances: Optimize PearsonR/SpearmanR

[ales-erjavec]

Issue

• PearsonR is poorly implemented by a double for loop in python.
• SpearmanR quadruples it's workload only to throw most of it away.

Description of changes

• Use numpy.corrcoef for PearsonR
• Implement a variants of corrcoef/spearmanr which compute correlations between two arrays more efficiently (without also computing all correlations within the two arrays).

Includes

• Code changes
• Tests
• Documentation

[codecov-io]

Codecov Report

Merging #2852 into master will increase coverage by 0.01%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master    #2852      +/-   ##
==========================================
+ Coverage   81.91%   81.92%   +0.01%     
==========================================
  Files         326      326              
  Lines       55997    56031      +34     
==========================================
+ Hits        45868    45903      +35     
+ Misses      10129    10128       -1

[thocevar]

This looks ok. Do you have any measurements of how much we gain with this re-implementation of what we previously handed over to numpy and scipy?

[thocevar]

Are these two cases (if, else) necessary? At first glance stats.spearmanr seems to (efficiently) handle the case of a missing second attribute.

[thocevar]

Never mind.

[ales-erjavec]

In [1]: import Orange, numpy

In [2]: d = Orange.data.Table(numpy.random.random(size=(200, 200)))

In [3]: %timeit Orange.distance.PearsonR(d)

Before

1.59 s ± 12.6 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

After

614 µs ± 84.3 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [1]: import Orange, numpy

In [2]: d = Orange.data.Table(numpy.random.random(size=(400, 200)))

In [3]: %timeit Orange.distance.SpearmanR(d[1:], d[:-1])

Before

201 ms ± 2.28 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

After

47.9 ms ± 1.82 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)