Sparse oblique (SPO), part of the top-ranked configuration of Google's Yggdrasil Decision Forests (YDF), improve the accuracy while maintaining interpretability of Random Forests (RF) and Gradient Boosted Trees (GBT) by scanning a sparse linear combination of features instead of a single feature. Because projections are sampled at runtime, training is significantly slower, as pre-run optimizations such as presorting cannot be used. We overhaul SPO training in YDF, first by fixing inefficiencies in the released version, achieving 2-5x speedup, then by devising two novel methods, one aimed at GBTs and the other at RFs: (1) Hierarchical AVX2 and AVX-512-vectorized histogram filling speeds up typical GBT-depth trees by up to 1.6x in SPO-GBT and 2x for SPO-RF, and (2) runtime-dynamic histograms between vectorized histograms and exact splits, speeds up deeper, RF depth-typical trees (depths 16 to purity) by up to 1.6x with no detectable effect on accuracy. Our optimizations bring SPO-RF training time on par with YDF's axis-aligned RF. We extensively evaluate on 8 natural and 11 synthetic datasets of up to 10.5 million rows and 1.6 million features, from depth 6 to purity, and open-source the implementation.

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