A Case for Library-Level $k$-Means Binning in Histogram Gradient-Boosted Trees

TMLR Paper5540 Authors

Abstract: Modern Gradient Boosted Decision Trees (GBDTs) accelerate split finding with histogram-based binning, which reduces complexity from $O(N\log N)$ to $O(N)$ by aggregating gradients into fixed-size bins. However, the predominant quantile binning strategy—designed to distribute data points evenly among bins—may overlook critical boundary values that could enhance predictive performance. In this work, we consider a novel approach that replaces quantile binning with a $k$-means discretizer initialized with quantile bins, and justify the swap with a proof showing how, for any $L$-Lipschitz function, k-means maximizes the worst-case explained variance of Y obtained when treating each bin as an atomic unit. We test this swap against quantile and uniform binning on 33 OpenML datasets plus synthetics that control for modality, skew, and bin budget. Across 18 regression datasets, k-means shows no statistically significant losses at the 5% level and wins in four cases—most strikingly a 55% MSE drop on one particularly skewed dataset—even though k-means' mean reciprocal rank (MRR) is slightly lower (0.65 vs 0.72). On the 15 classification datasets the two methods are statistically tied (MRR 0.70 vs 0.68) with gaps $\leq$0.2 pp. Synthetic experiments confirm consistently large MSE gains—typically $>$20% and rising to 90% as outlier magnitude increases or bin budget drops. We find that k-means keeps error on par with exhaustive (no-binning) splitting when extra cuts add little value, yet still recovers key split points that quantile overlooks. As such, we advocate for a built-in bin_method=$k$-means flag, especially in regression tasks and in tight-budget settings such as the 32–64-bin GPU regime—because it is a "safe default" with large upside, yet adds only a one-off, cacheable overhead ($\approx$ 3.5s to bin 10M rows on one Apple M1 thread).

Submission Length: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Ilan_Shomorony1

Submission Number: 5540