# ndscape: a structural map of the nested dichotomy space

arXiv: https://arxiv.org/abs/2610.18050 · HTML: https://mlsanity.com/paper/2610.18050/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 41 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 2 of 2)

- [Using simulation studies to evaluate statistical methods](https://mlsanity.com/paper/1712.03198/) (2017)
- [Building Ensembles of Adaptive Nested Dichotomies with Random-Pair Selection](https://mlsanity.com/paper/1604.01854/) (2016)

## Abstract (arXiv)

Nested dichotomies (NDs) reduce multiclass classification to a tree of binary classifiers. Tree structure can change accuracy, bias, and variance, but the full space of structures has not been mapped in aggregate. We introduce ndscape, a two-dimensional mapping of ND structures based on depth-weighted structural tokens. We use this embedding to conduct what is, to our knowledge, the first bias-variance analysis across the ND structure space. In simulations with 6 to 10 classes, NDs with similar tree structures exhibit similar squared bias, variance, and squared probability loss, regardless of whether the binary classifier is logistic regression or a decision tree. Variance, however, follows mean root-to-leaf depth when logistic regression is used at each node, so flatter, more balanced NDs are more stable, whereas with decision-tree node models, variance is not associated with depth and differs little across ND structures. On six datasets with 6 to 19 classes, held-out accuracy, log loss, and prediction variance remain spatially organised on the same topology-only map. None of the six standard construction heuristics tested selects a tree from the best-performing cluster on any dataset, although some select high-performing individual trees. The ndscape embedding turns ND selection from one opaque construction step into a readable comparison of class groupings, exposing the upper-level splits that distinguish high-performing and stable regions.