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Thank you for information, NGBoost looks interesting.
Currently, oneDAL does not have same patching functionality for LightGBM and XGBoost as for sklearn, but this direction is promising.
Theoretically, you can implement estimator inherited from LightGBM and implement custom predict and predict_proba methods using daa4py functions
I have come across speed-ups for XGBoost and LightGBM here and wondered if it similar sppedups could be achieved for NGBoost with LightGBM as a base learner. https://stanfordmlgroup.github.io/projects/ngboost/
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