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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2502.18167 |
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| _version_ | 1866910958390083584 |
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| author | Shao, Xiao Wu, Guoqiang |
| author_facet | Shao, Xiao Wu, Guoqiang |
| contents | In multi-task learning (MTL) with each task involving graph-dependent data, existing generalization analyses yield a \emph{sub-optimal} risk bound of $O(\frac{1}{\sqrt{n}})$, where $n$ is the number of training samples of each task. However, to improve the risk bound is technically challenging, which is attributed to the lack of a foundational sharper concentration inequality for multi-graph dependent random variables. To fill up this gap, this paper proposes a new Bennett-type inequality, enabling the derivation of a sharper risk bound of $O(\frac{\log n}{n})$. Technically, building on the proposed Bennett-type inequality, we propose a new Talagrand-type inequality for the empirical process, and further develop a new analytical framework of the local fractional Rademacher complexity to enhance generalization analyses in MTL with multi-graph dependent data. Finally, we apply the theoretical advancements to applications such as Macro-AUC optimization, illustrating the superiority of our theoretical results over prior work, which is also verified by experimental results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18167 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharper Risk Bound for Multi-Task Learning with Multi-Graph Dependent Data Shao, Xiao Wu, Guoqiang Machine Learning In multi-task learning (MTL) with each task involving graph-dependent data, existing generalization analyses yield a \emph{sub-optimal} risk bound of $O(\frac{1}{\sqrt{n}})$, where $n$ is the number of training samples of each task. However, to improve the risk bound is technically challenging, which is attributed to the lack of a foundational sharper concentration inequality for multi-graph dependent random variables. To fill up this gap, this paper proposes a new Bennett-type inequality, enabling the derivation of a sharper risk bound of $O(\frac{\log n}{n})$. Technically, building on the proposed Bennett-type inequality, we propose a new Talagrand-type inequality for the empirical process, and further develop a new analytical framework of the local fractional Rademacher complexity to enhance generalization analyses in MTL with multi-graph dependent data. Finally, we apply the theoretical advancements to applications such as Macro-AUC optimization, illustrating the superiority of our theoretical results over prior work, which is also verified by experimental results. |
| title | Sharper Risk Bound for Multi-Task Learning with Multi-Graph Dependent Data |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.18167 |