# (α,β)-Stability for Boosting Vector-Valued Prediction

arXiv: https://arxiv.org/abs/2602.18866 · HTML: https://mlsanity.com/paper/2602.18866/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 21 Feb 2026.

## Builds on (most cited first, 7 of 7)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [A Characterization of Multiclass Learnability](https://mlsanity.com/paper/2203.01550/) (2022)
- [Sub-Gaussian estimators of the mean of a random vector](https://mlsanity.com/paper/1702.00482/) (2017)
- [A Characterization of List Learnability](https://mlsanity.com/paper/2211.04956/) (2022)
- [Multiclass Boosting: Simple and Intuitive Weak Learning Criteria](https://mlsanity.com/paper/2307.00642/) (2023)
- [Of Dice and Games: A Theory of Generalized Boosting](https://mlsanity.com/paper/2412.08012/) (2024)
- [StructBoost: Boosting Methods for Predicting Structured Output Variables](https://mlsanity.com/paper/1302.3283/) (2013)

## Abstract (arXiv)

Despite the widespread use of boosting in structured prediction, a general theoretical understanding of aggregation beyond scalar prediction remains incomplete. We study vector-valued prediction under a target divergence and identify a geometric stability property under which aggregation amplifies weak guarantees into strong ones. We formalize this property as (α,β)-stability by geometric median and show how it supports a boosting framework based on exponential reweighting and geometric-median aggregation. For vector-valued prediction, we characterize this stability property under several natural divergences: ℓ1 and ℓ2 distances for unconstrained vector-valued prediction, and TV, Hellinger, and KL for density estimation over finite probability vectors. Building on these results, we propose a generic boosting framework geomedboost. Under a weak learner condition and (α,β)-stability, we obtain exponential decay of the empirical divergence error, which then yields population guarantees through a generalization bound.