Add the feature contribution argument output as an option at predict

[Fish-Soup]

Add the option to call lightGBM.Booster.predict(...., pred_contrib=True)
This generates an output with the number of columns = the number distribution arguments * (number of features + 1).

Output is converted to a multi-index column of two levels, distribution args and feature contributions (and Constant)

Unit test added for pred_contributions to test if when you sum up all contributions and apply response function you get the same result as when predicting the parameters.

I also noticed that when predicting sampling is always applied even if we are returning an output that does not require sampling. This must make predictions a little slower on larger data sets. As such I moved the sampling code so it only gets called when required.

[StatMixedML]

Thanks for opening the PR and for your interest in the proect, very much appreciated!

I`d need some time, though, to look into it in detail.

May I ask you to also give an example of how to use and interpret it. That would help, thanks!

[Fish-Soup]

Hi I added an example in the examples section. There is lots more you can use the output for. At a very high level it provides SHAP like information but directly from lightGBM's internal calculations. When a distribution_arg is used we can also use it to get the actual contribution to the final parameter value

[Fish-Soup]

I've added a little code to give the pandas columns a level name based on the pred_type argument. This is helpful when doing pandas operations like stack.

For example when pred_type="quantiles", the pandas output columns will have name "quantiles". This means we can

pred_samples.stack("quantiles") to create a multi index series.

Ive also changed the names for the multi-index with pred_type="contributions" to ["parameters", "feature_contributions"] from ["distribution_args", "FeatureContributions"] to alligh with the pred_type naming convention

[StatMixedML]

Thanks for your changses. I am currently occupied with the Hyper-Tree paper, so please do expect some delay in my review.

[Fish-Soup]

Is there anything I can do to help speed it along? The PR is unit tested and is essentially just passing arguments to lightgbm.booster then doing some reshaping of the output.