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Sparse Covariance Matrix Estimation by DCA-Based Algorithms.

Duy Nhat Phan1, Hoai An Le Thi2, Tao Pham Dinh3

  • 1Laboratory of Theoretical and Applied Computer Science EA 3097, University of Lorraine, Ile du Saulcy, 57045 Metz, France duy-nhat.phan@univ-loraine.fr.

Neural Computation
|September 29, 2017
PubMed
Summary
This summary is machine-generated.

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This study introduces a new method for sparse covariance matrix estimation using [Formula: see text]-norm regularization. The proposed approach effectively handles nonconvex objective functions, outperforming existing methods in classification and portfolio optimization tasks.

Area of Science:

  • Statistics
  • Optimization
  • Machine Learning

Background:

  • Sparse Covariance Matrix Estimation (SCME) is crucial in high-dimensional data analysis.
  • Traditional methods struggle with the nonconvex and discontinuous nature of the [Formula: see text]-norm regularization.
  • Efficient SCME is vital for applications like discriminant analysis and portfolio optimization.

Purpose of the Study:

  • To propose a novel approach for SCME using [Formula: see text]-norm regularization.
  • To address the challenges posed by nonconvexity and discontinuity in the SCME objective function.
  • To develop and evaluate efficient algorithms for SCME.

Main Methods:

  • Utilizing difference of convex functions (DC) approximations for the [Formula: see text]-norm.

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  • Applying DC programming and the DC algorithm (DCA) to nonconvex SCME problems.
  • Developing two distinct DC formulations and corresponding DCA schemes.

    • Main Results:

    • The proposed DC formulations and DCA schemes effectively solve nonconvex SCME problems.
    • Empirical experiments on simulated and real data demonstrate the algorithms' efficiency.
    • The novel approach shows superiority compared to seven state-of-the-art methods.

    Conclusions:

    • The proposed DC-based approach provides an effective solution for SCME with [Formula: see text]-norm regularization.
    • The developed DCA schemes are efficient and outperform existing methods.
    • This work advances SCME for applications in sparse quadratic discriminant analysis and portfolio optimization.