ML Math Derivations (12): XGBoost and LightGBM

Sat, 31 Jan 2026 09:00:00 +0000

XGBoost and LightGBM are the two libraries that quietly win most tabular-data battles — on Kaggle leaderboards, in fraud-detection pipelines, in ad ranking, in churn models. They share the same backbone (gradient-boosted trees, Part 11 ) but make very different engineering bets:

XGBoost sharpens the math: it brings the second derivative of the loss into the objective, regularises the tree itself, and turns split selection into a closed-form score.
LightGBM sharpens the systems: it bins features into a small histogram, grows trees leaf-by-leaf, throws away uninformative samples (GOSS) and bundles mutually exclusive sparse features (EFB).

The result is two tools that look interchangeable from the API but behave very differently when $$N$$ or $$d$$ becomes large. This post derives every formula behind those choices so you can read a tuning guide and know why each knob exists.

Gradient Boosting on Chen Kai Blog

ML Math Derivations (12): XGBoost and LightGBM