LinXGBoost: Extension of XGBoost to Generalized Local Linear Models

XGBoost is often presented as the algorithm that wins every ML competition. Surprisingly, this is true even though predictions are piecewise constant. This might be justified in high dimensional input spaces, but when the number of features is low, a piecewise linear model is likely to perform better. XGBoost was extended into LinXGBoost that stores at each leaf a linear model. This extension, equivalent to piecewise regularized least-squares, is particularly attractive for regression of functions that exhibits jumps or discontinuities. Those functions are notoriously hard to regress. Our extension is compared to the vanilla XGBoost and Random Forest in experiments on both synthetic and real-world data sets.