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New research defines limits for learning linear operators

By PulseAugur Editorial · [2 sources] ·

Researchers have established the statistical and computational limits for learning bounded linear operators between Sobolev spaces using noisy input-output data. The problem is reframed as an infinite-dimensional matrix regression with a complex multiscale structure. A novel blockwise least-squares estimator has been developed that achieves optimal rates and computational efficiency by adapting sample sizes to different scales. AI

RANK_REASON The cluster contains an academic paper published on arXiv detailing theoretical research in statistics and machine learning.

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

COVERAGE [2]

  1. arXiv stat.ML TIER_1 English(EN) · Jiaheng Chen, Daniel Sanz-Alonso ·

    Optimal Multiscale Learning of Linear Operators

    arXiv:2606.16913v1 Announce Type: cross Abstract: We study the statistical and computational limits of learning bounded linear operators between Sobolev spaces from noisy input-output data. In wavelet coordinates, the problem is recast as an infinite-dimensional matrix regression…

  2. arXiv stat.ML TIER_1 English(EN) · Daniel Sanz-Alonso ·

    Optimal Multiscale Learning of Linear Operators

    We study the statistical and computational limits of learning bounded linear operators between Sobolev spaces from noisy input-output data. In wavelet coordinates, the problem is recast as an infinite-dimensional matrix regression problem with a heterogeneous two-sided multiscale…

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