[_pastel]

Because anytime I search for literature on basic tweaks to the structure of decision trees, I find nothing.

Another example: modern GBM implementations all use binary trees. How would they perform with ternary trees? Or k-way trees for larger k plus some additional soft penalty that encourages minimizing the number branches, unless the information gain is really worth it?

(You can simulate ternary trees with binary, but the splitting behavior is different because ternary can more easily identify good splitting regions in the middle range of the histogram values.)

This seems like such a basic structural question, but the only relevant search result was this downvoted Stack Exchange question from 5 years ago: https://stats.stackexchange.com/questions/305685/ternary-dec...

There are lots of papers on ternary trees in old-school contexts like Ternary Decision Diagrams etc., but nothing relevant to the context of modern tree ensemble performance. Or maybe I'm just bad at searching?

(I implemented this and saw a small accuracy increase from ternary on large datasets, but much worse training speed because you get less mileage from the histogram subtraction trick. Maybe the accuracy would be even better with a more clever choice of soft penalty.)