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Sure independence screening and compressed random sensing

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  • Lingzhou Xue
  • Hui Zou

Abstract

Compressed sensing is a very powerful and popular tool for sparse recovery of high dimensional signals. Random sensing matrices are often employed in compressed sensing. In this paper we introduce a new method named aggressive betting using sure independence screening for sparse noiseless signal recovery. The proposal exploits the randomness structure of random sensing matrices to greatly boost computation speed. When using sub-Gaussian sensing matrices, which include the Gaussian and Bernoulli sensing matrices as special cases, our proposal has the exact recovery property with overwhelming probability. We also consider sparse recovery with noise and explicitly reveal the impact of noise-to-signal ratio on the probability of sure screening. Copyright 2011, Oxford University Press.

Suggested Citation

  • Lingzhou Xue & Hui Zou, 2011. "Sure independence screening and compressed random sensing," Biometrika, Biometrika Trust, vol. 98(2), pages 371-380.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:2:p:371-380
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    File URL: http://hdl.handle.net/10.1093/biomet/asr010
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    Cited by:

    1. Xiangyu Wang & Chenlei Leng, 2016. "High dimensional ordinary least squares projection for screening variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 589-611, June.
    2. Lin, Lu & Sun, Jing, 2016. "Adaptive conditional feature screening," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 287-301.
    3. Arun Srinivasan & Lingzhou Xue & Xiang Zhan, 2021. "Compositional knockoff filter for high‐dimensional regression analysis of microbiome data," Biometrics, The International Biometric Society, vol. 77(3), pages 984-995, September.

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