Adding prediction intervals for GradientBoostingRegressor and review RandomForest prediction intervals - https://alice.its.cern.ch/jira/browse/ATO-459 about rootinteractive HOT 4 OPEN

In order to include new regression, classifiers - MLpipeline code to be restructured
https://alice.its.cern.ch/jira/browse/ATO-459

Current version (TO BE deprecated)

• design influenced by TMVA - does not scale
• fitter, regressor created in fit function based on the names and options
  • method parameter defined in Register_Method
  • model created during the fit method
  • many if, does not scale

New version - to be implemented

• models (regression, quantile regression wrappers) to be constructed by users
• wrappers implement additional common functionality
• models registered in Register_model
• models reused for fits

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Reference - GradientBoostingRegressor https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.GradientBoostingRegressor.html

quantiles obtained during training time - using appropriate cost function

loss{‘ls’, ‘lad’, ‘huber’, ‘quantile’}, default=’ls’

loss function to be optimized. ‘ls’ refers to least squares regression. ‘lad’ (least absolute deviation) is a highly robust loss
function solely based on order information of the input variables. ‘huber’ is a combination of the two. ‘quantile’ allows quantile > regression (use alpha to specify the quantile).

Other References

https://towardsdatascience.com/regression-prediction-intervals-with-xgboost-428e0a018b
https://heartbeat.fritz.ai/5-regression-loss-functions-all-machine-learners-should-know-4fb140e9d4b0
https://www.evergreeninnovations.co/blog-quantile-loss-function-for-machine-learning/

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Deep quantile regression:

based on the cost function discussed in the: 

https://alice.its.cern.ch/jira/browse/ATO-459?focusedCommentId=253647&page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel#comment-253647 

• Blogs:
  • https://towardsdatascience.com/deep-quantile-regression-c85481548b5a
  • https://www.evergreeninnovations.co/blog-quantile-loss-function-for-machine-learning/

describe scalar version - one quantile per Neural network.

Quantile vector implementation in Jupyter notebook:
https://github.com/strongio/quantile-regression-tensorflow/blob/master/Quantile%20Loss.ipynb

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Quantile regression interface:

In general - quantiles should be defined before fitting (not needed in the Scikit -garden - but skgradern not supported anymore)

BDTs and neural nets should be constructed knowing which quantiles are needed

• BDTs
  • For BDT array of the regressor to be created for each quantile
• Deep neural nets options
  • Array of neural nets create for each quantile:
    • Slower - 
    • Non consistent - quantiles prediction could be not sorted
    • Bigger variance
  • One neural net for all quantile predictions

Proposed interface:

• init
• fit
• predict(+index)
• appendStatPandas(options)
  • append statistics to the panda data frame
  • by default all options
• RMS estimators based on the quantiles
  • some approximation has to be done
    appendStatTree ?
  • append statistic to the tree for later usage

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