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Researchers solve open problem in weighted data selection for linear regression

By PulseAugur Editorial · [1 sources] ·

Researchers Hanneke, Moran, Shlimovich, and Yehudayoff have determined the exact risk ratios for weighted data selection in linear regression for specific cases within the open regime of $d < n < 2d$. They proved that $F_w(d, 2d-1) = 1 + 1/d$, confirming a previous claim, and also found exact values for $F_w(3,4) = 5/3$ and $F_w(4,5) = 2$. The study provides a lower bound of $F_w(d, d+k) less 1 + ext{HarmonicQuantity}(d,k)$ and conjectures this bound is the minimax value for datasets with orthogonal circuit-block structure in their whitened gradient systems. The proofs utilize geometric arguments, including rigidity theorems and classifications of positive bases. AI

IMPACT Provides theoretical advancements in data selection for linear regression, potentially impacting future algorithm development.

RANK_REASON Academic paper detailing mathematical proofs and solutions to an open problem in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Researchers solve open problem in weighted data selection for linear regression

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Academic paper detailing mathematical proofs and solutions to an open problem in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. 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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