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Two papers resolve open problems in weighted data selection for linear regression

By PulseAugur Editorial · [3 sources] ·

Two new papers published on arXiv address open problems in weighted data selection for linear regression. The first paper resolves a threshold question posed at COLT 2025, proving that $(m+1)d$ weighted examples are exactly sufficient for recovering full-data loss in vector-valued linear regression. The second paper determines exact risk ratios for weighted data selection in linear regression for several cases, including confirming a claim for $F_w(d, 2d-1) = 1 + 1/d$ and providing new values for $F_w(3,4)$ and $F_w(4,5)$. Both papers introduce novel upper-bound techniques and provide structural evidence for their conjectures. AI

IMPACT These papers advance theoretical understanding in machine learning, potentially influencing future algorithm design and data selection strategies.

RANK_REASON Two academic papers published on arXiv addressing specific mathematical problems in machine learning.

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 3 sources. How we write summaries →

Two papers resolve open problems in weighted data selection for linear regression

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COVERAGE [3]

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

    Exact Recovery Thresholds for Weighted Data Selection in Vector-Valued Linear Regression

    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) ·

    Exact Recovery Thresholds for Weighted Data Selection in Vector-Valued Linear Regression

    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 ·

    Exact Risk Ratios for Weighted Data Selection in Linear Regression

    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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