Add LASSO without structure to LinearRegression notebook

[Blunde1]

Showcases how to resolve equinor/ert#6599
I think the case for LASSO is well argued for there. Unfortunately I do not know of any reference papers doing this.
The case for LASSO can be seen e.g. from

• Presentation at EnKF: chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://ncda-fs.web.norce.cloud/WS2023/raanes.pdf
• • EnKF = Monte Carlo + LLS.
• Transport methods: https://arxiv.org/pdf/2210.17000.pdf
• • We really do want to fit a multivariate Gaussian
• When doing statistical fitting (fit multivariate Gaussian) we must control the degrees of freedom
• • LLS is inferior to LASSO (and others, e.g. RIDGE), when we are not in the asymptotic case. Model selection as part of the objective, etc.

Thus it makes sense to improve upon EnKF and ES ++ by doing Monte Carlo + LASSO (or Ridge or similar).

[Blunde1]

The docs build is failing, I guess because I import graphite-maps? Will copy the imported linear_l1_regression function so that we avoid the import.

[tommyod]

Not sure why it fails now. I see no error message... Try running locally

sphinx-build -c docs/source/ -b html docs/source/ docs/build/html -W

[Blunde1]

Not sure why it fails now. I see no error message... Try running locally

sphinx-build -c docs/source/ -b html docs/source/ docs/build/html -W

I see I need Java for the docs? (pandoc) Is there no way around this?

From checking the CI I see

Warning, treated as error:
/home/runner/work/iterative_ensemble_smoother/iterative_ensemble_smoother/docs/source/LinearRegression.ipynb:Executing notebook failed: CellExecutionError [mystnb.exec]

perhaps I import or use something in the notebook that is not part of the pip install .[doc] requirements?
Edit: perhaps sklearn

[tommyod]

Added some comments!

[dafeda]

Suggested change

	However, multiple (Kalman) ensemble methods only produce an estiamte $K$ either explicit or explicit,
	However, multiple (Kalman) ensemble methods only produce an estimate $K$ either explicit or implicit,

Not sure I understand this sentence.
Do you mean that several different ensemble methods only produce an estimate of $K$ without specifying covariance structure?
What do you mean by explicit / implicit?