Sparse Covariance Matrix Estimation by DCA-Based Algorithms.

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.
• 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.