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New algorithms improve John ellipsoid approximation accuracy

By PulseAugur Editorial · [2 sources] ·

Researchers have developed new algorithms for approximating the John ellipsoid of a symmetric polytope, improving upon existing leverage-score methods. These algorithms separate the complexity of computation into distinct costs: certification, identification, and accuracy. The new approach offers a significantly faster convergence rate for accuracy, reducing it to a doubly logarithmic dependence on the approximation parameter \(\varepsilon\) after an initial setup phase. AI

IMPACT This research could lead to more efficient computational methods in related fields, potentially impacting AI applications that rely on optimization and geometric approximation.

RANK_REASON The cluster contains an academic paper detailing new algorithms and theoretical advancements in a specific area of mathematics and computational learning theory. [lever_c_demoted from research: ic=2 ai=0.4]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

New algorithms improve John ellipsoid approximation accuracy

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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Xiaoyu Li, Junwei Yu, Jiaojiao Jiang, Junbin Gao, Andi Han ·

    Beyond Averaging in John Ellipsoid Approximation: High-Accuracy Algorithms in the Leverage-Score Model

    arXiv:2606.20082v1 Announce Type: cross Abstract: The John ellipsoid of a symmetric polytope $P=\{\mathbf{x}\in\mathbb{R}^d:\|\mathbf{A}\mathbf{x}\|_\infty\le1\}$, $\mathbf{A}\in\mathbb{R}^{n\times d}$, is computed by a long line of leverage-score algorithms, from Cohen, Cousins,…

  2. arXiv cs.LG TIER_1 English(EN) · Andi Han ·

    Beyond Averaging in John Ellipsoid Approximation: High-Accuracy Algorithms in the Leverage-Score Model

    The John ellipsoid of a symmetric polytope $P=\{\mathbf{x}\in\mathbb{R}^d:\|\mathbf{A}\mathbf{x}\|_\infty\le1\}$, $\mathbf{A}\in\mathbb{R}^{n\times d}$, is computed by a long line of leverage-score algorithms, from Cohen, Cousins, Lee and Yang (COLT 2019) to its successors [WY24,…

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