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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.18866 |
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| _version_ | 1866914553402490880 |
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| author | Qian, Jian Ge, Shu |
| author_facet | Qian, Jian Ge, Shu |
| contents | 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: $\ell_1$ and $\ell_2$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18866 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $(α,β)$-Stability for Boosting Vector-Valued Prediction Qian, Jian Ge, Shu Machine Learning 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: $\ell_1$ and $\ell_2$ 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. |
| title | $(α,β)$-Stability for Boosting Vector-Valued Prediction |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.18866 |