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Common reducing subspace model and network alternation analysis

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  • Wenjing Wang
  • Xin Zhang
  • Lexin Li

Abstract

Motivated by brain connectivity analysis and many other network data applications, we study the problem of estimating covariance and precision matrices and their differences across multiple populations. We propose a common reducing subspace model that leads to substantial dimension reduction and efficient parameter estimation. We explicitly quantify the efficiency gain through an asymptotic analysis. Our method is built upon and further extends a nascent technique, the envelope model, which adopts a generalized sparsity principle. This distinguishes our proposal from most xisting covariance and precision estimation methods that assume element‐wise sparsity. Moreover, unlike most existing solutions, our method can naturally handle both covariance and precision matrices in a unified way, and work with matrix‐valued data. We demonstrate the efficacy of our method through intensive simulations, and illustrate the method with an autism spectrum disorder data analysis.

Suggested Citation

  • Wenjing Wang & Xin Zhang & Lexin Li, 2019. "Common reducing subspace model and network alternation analysis," Biometrics, The International Biometric Society, vol. 75(4), pages 1109-1120, December.
  • Handle: RePEc:bla:biomet:v:75:y:2019:i:4:p:1109-1120
    DOI: 10.1111/biom.13099
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    Cited by:

    1. Bingkai Wang & Xi Luo & Yi Zhao & Brian Caffo, 2021. "Semiparametric partial common principal component analysis for covariance matrices," Biometrics, The International Biometric Society, vol. 77(4), pages 1175-1186, December.
    2. Pan, Yuqing & Mai, Qing, 2020. "Efficient computation for differential network analysis with applications to quadratic discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    3. Alexander M. Franks, 2022. "Reducing subspace models for large‐scale covariance regression," Biometrics, The International Biometric Society, vol. 78(4), pages 1604-1613, December.

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