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English(EN) Exact Recovery Thresholds for Weighted Data Selection in Vector-Valued Linear Regression

两篇论文解决了加权数据选择线性回归中的开放性问题

作者 PulseAugur 编辑部 · [3 个来源] ·

arXiv上发表的两篇新论文解决了加权数据选择线性回归中的开放性问题。第一篇论文解决了COLT 2025上提出的一个阈值问题，证明了$(m+1)d$个加权样本对于恢复向量值线性回归中的全数据损失是精确足够的。第二篇论文确定了线性回归中加权数据选择的精确风险比，包括几种情况，例如确认了$F_w(d, 2d-1) = 1 + 1/d$的说法，并提供了$F_w(3,4)$和$F_w(4,5)$的新值。两篇论文都引入了新的上界技术，并为它们的猜想提供了结构性证据。 AI

影响 这些论文推进了机器学习的理论理解，可能影响未来的算法设计和数据选择策略。

排序理由 两篇发表在arXiv上的学术论文，解决了机器学习中的特定数学问题。

在 arXiv cs.LG 阅读 →

AI 生成摘要 · Google Gemini · 来自 3 个来源。 我们如何撰写摘要 →

两篇论文解决了加权数据选择线性回归中的开放性问题

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报道来源 [3]

  1. arXiv cs.LG TIER_1 English(EN) · Guangjian Zhang ·

    向量值线性回归中加权数据选择的确切恢复阈值

    arXiv:2608.30254v1 Announce Type: new Abstract: We resolve the threshold part of Question 4 of the COLT 2025 open problem "Data Selection for Regression Tasks" of Hanneke, Moran, Shlimovich and Yehudayoff. In vector-valued linear regression with square loss $\ell_{(x,y)}(W)=|Wx-y…

  2. Hugging Face Daily Papers TIER_1 English(EN) ·

    向量值线性回归的加权数据选择的精确恢复阈值

    We resolve the threshold part of Question 4 of the COLT 2025 open problem "Data Selection for Regression Tasks" of Hanneke, Moran, Shlimovich and Yehudayoff. In vector-valued linear regression with square loss $\ell_{(x,y)}(W)=|Wx-y|_2^2$, where $x\in\mathbb{R}^d$, $y\in\mathbb{R…

  3. arXiv cs.LG TIER_1 English(EN) · Guangjian Zhang ·

    线性回归中加权数据选择的精确风险比率

    arXiv:2608.28007v1 Announce Type: new Abstract: Hanneke, Moran, Shlimovich and Yehudayoff (COLT 2025) posed the following open problem. A selector sees a finite dataset $D \subseteq \mathbb{R}^d \times \mathbb{R}$, picks at most $n$ examples together with nonnegative weights, and…

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