Math Behind GOSS (Gradient-Based One Side Sampling)? As per my understanding through books &amp; Google Search,

GOSS (Gradient-Based One Side Sampling) is a novel sampling method that downsamples the instances on the basis of gradients. As we
know instances with small gradients are well trained (small training
error) and those with large gradients are undertrained. A naive
approach to downsample is to discard instances with small gradients by
solely focussing on instances with large gradients but this would
alter the data distribution. In a nutshell, GOSS retains instances
with large gradients while performing random sampling on instances
with small gradients. Source

LightGBM uses a novel technique of Gradient-based One-Side Sampling (GOSS) to filter out the data instances for finding a split value while XGBoost uses pre-sorted algorithm &amp; Histogram-based algorithm for computing the best split.

Can someone please explain the math behind GOSS?
Wang et al., (2019) have provided a nice and clear explanation. Please, check out their paper to find the answer you are looking for:
Part II. BAYESIAN OPTIMIZED LIGHTGBM
Section: A. The Principle of the LightGBM
Wang, R., Liu, Y., Ye, X., Tang, Q., Gou, J., Huang, M., &amp; Wen, Y. (2019). Power System Transient Stability Assessment Based on Bayesian Optimized LightGBM. 2019 IEEE 3Rd Conference On Energy Internet And Energy System Integration (EI2). doi: 10.1109/ei247390.2019.9062027