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Research paper reveals limitations of restricted eigenvalue bounds for heavy-tailed data

By PulseAugur Editorial · [1 sources] ·

A new research paper explores the limitations of restricted eigenvalue (RE) bounds, which are crucial for stable recovery in norm-regularized estimators. The study demonstrates that for heavy-tailed designs, the sample size required for these bounds to hold does not follow the same law as for Gaussian measurements. Specifically, the paper shows that a constant-width polyhedral descent cone with fixed small-ball constants can have zero empirical RE on every sample path up to half the ambient dimension. The research quantifies the sharp worst-case sample complexity for such scenarios, indicating a significant difference in sample requirements compared to Gaussian designs. AI

IMPACT This research may impact the theoretical understanding and practical application of machine learning algorithms that rely on norm-regularized estimators, particularly when dealing with non-Gaussian data distributions.

RANK_REASON The cluster contains a single academic paper published on arXiv. [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 →

Research paper reveals limitations of restricted eigenvalue bounds for heavy-tailed data

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The cluster contains a single academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Shi Fu, Huibo Xu, Qixin Zhang, Dacheng Tao ·

    Restricted Eigenvalues Beyond Gaussian Width: Threshold Occupancy under Heavy Tails

    arXiv:2609.03504v1 Announce Type: new Abstract: Restricted eigenvalue (RE) bounds govern stable recovery by norm-regularized estimators. For isotropic sub-Gaussian measurements, the benchmark sample size is $1+w(A)^2$, where $w(A)$ is the Gaussian width of the normalized descent …

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