Prediction outside prediction interval with LGBMRegressor

[masakljun]

Description

I am using LGBMRegressor to obtain predictions and prediction intervals as suggested in an article https://developer.ibm.com/articles/prediction-intervals-explained-a-lightgbm-tutorial/. However, the issue I am having is that the predicted point (with alpha set to 0.5) is sometimes outside the prediction interval (alpha = 0.05 and alpha = 0.95). I suppose this is due to the issue of "crossing quantiles", however, I am wondering if there is any fix for this? Thanks in advance!

Reproducible example

Can't share data due to data policy at company.

reg = lgb.LGBMRegressor(objective = 'quantile', alpha = 0.5, learning_rate = 0.05, max_depth = 15, n_estimators = 900, random_state = 0).fit(X_train, y_train)

lower = lgb.LGBMRegressor(objective = 'quantile', alpha = 0.05, learning_rate = 0.05, max_depth = 15, n_estimators = 900, random_state = 0).fit(X_train, y_train)

upper = lgb.LGBMRegressor(objective = 'quantile', alpha = 0.95, learning_rate = 0.05, max_depth = 15, n_estimators = 900, random_state = 0).fit(X_train, y_train)

Environment info

LightGBM version or commit hash:
'3.3.2'

Command(s) you used to install LightGBM
pip install lightgbm

[jmoralez]

We already have this as a feature request in #3447 and #4201. The problem is described here: #3447 (comment)

[github-actions]

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