add LinearRegression class

[mathause]

• Closes #xxx
• Tests added
• Passes isort . && black . && flake8
• Fully documented, including CHANGELOG.rst

This adds a LinearRegression class. To fit a linear regression you would call:

lr = mesmer.core.linear_regression.LinearRegression()
lr.fit({"tas": tas}, target, "time")
lr.params

This sets lr.params - i.e. the estimated intercept and slope for tas.

The next examples for one gridpoint ("cell") actually work - you can manually set lt.params and then call lr.predict and lr.residuals to get the predicted values and the residuals:

import mesmer.core.linear_regression
import xarray as xr

# set some params (i.e. intercept and slope)
lr = mesmer.core.linear_regression.LinearRegression()

params = xr.Dataset(data_vars={"intercept": ("cell", [5]), "tas": ("cell", [0.1])})
lr.params = params

tas_predictor = xr.DataArray([0, 1, 2], dims="time")
target = xr.DataArray([[5, 8, 0]], dims=("cell", "time"))


predicted = lr.predict({"tas": tas_predictor})
residuals = lr.residuals({"tas": tas_predictor}, target)

[codecov-commenter]

Codecov Report

Merging #134 (d772b60) into master (a682256) will increase coverage by 0.45%.
The diff coverage is 89.85%.

@@            Coverage Diff             @@
##           master     #134      +/-   ##
==========================================
+ Coverage   78.97%   79.43%   +0.45%     
==========================================
  Files          29       29              
  Lines        1346     1405      +59     
==========================================
+ Hits         1063     1116      +53     
- Misses        283      289       +6     

Flag	Coverage Δ
unittests	79.43% <89.85%> (+0.45%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
mesmer/core/linear_regression.py	90.00% <83.33%> (-10.00%)	⬇️
mesmer/core/utils.py	100.00% <100.00%> (+5.88%)	⬆️
mesmer/calibrate_mesmer/train_gv.py	85.33% <0.00%> (+0.40%)	⬆️
mesmer/create_emulations/create_emus_gv.py	73.46% <0.00%> (+1.73%)	⬆️

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[mathause]

This is basically an xarray wrapper for from sklearn.linear_model.LinearRegression.

[mathause]

@yquilcaille If you are interested you can have a look here. You can concentrate on the linear_regression.py file - the others are not super important.

[znicholls]

Looks sick, such a nice and elegant solution to how we store parameters, make the fitting and prediction stay close to each other etc. Not sure if there's changelog etc. to be done but I think this is a great pattern for us to follow

[znicholls]

I um and ah about this. I think it's probably a good idea to just get people used to the pattern of calling fit and then getting the params or whatever in the next line. That's what's used in sklearn and following that is probably a good idea. We could add a function like this to the codebase of course, it's so simple that it probably doesn't hurt...

[mathause]

Yes, I recently heard somewhere that a class method should either return something or change state but not both. So I will keep it as is.

[mathause]

Thanks for the feedback! Will add a changelog and merge. I am not yet sure if the AR process will work you just as nice...