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Meshes that trap random subspaces

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arxiv 1304.0003 v1 pith:BR75C3TT submitted 2013-03-29 cs.IT math.ITmath.OCmath.PR

Mihailo Stojnic This is my paper · ORCID
classification cs.ITmath.ITmath.OCmath.PR
keywords citeresultsolvingsystemsusedclassicconsideredcontext
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abstract

In our recent work \cite{StojnicCSetam09,StojnicUpper10} we considered solving under-determined systems of linear equations with sparse solutions. In a large dimensional and statistical context we proved results related to performance of a polynomial $\ell_1$-optimization technique when used for solving such systems. As one of the tools we used a probabilistic result of Gordon \cite{Gordon88}. In this paper we revisit this classic result in its core form and show how it can be reused to in a sense prove its own optimality.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Information-theoretic limits and approximate message-passing for high-dimensional time series

    cs.IT 2025-01 conditional novelty 6.0 of 10

    The paper proves a variational formula for the mutual information in high-dimensional linear regression with AR(1) dependent rows, and shows empirically that VAMP often reaches the predicted optimal error.

  2. Deep ReLU networks -- injectivity capacity upper bounds

    stat.ML 2024-12 reject novelty 6.0 of 10

    For deep ReLU networks with random Gaussian weights, the paper gives upper bounds on the layer expansion needed for injectivity and finds the expansion need saturates by four layers.

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