Application of regularized covariance matrices in logistic regression and portfolio optimization

Area of Science:

• Statistics
• Machine Learning
• Financial Mathematics

Background:

• Covariance estimation is vital for logistic regression and portfolio optimization.
• High-dimensional or small-sample data often leads to non-invertible covariance matrices, hindering model performance.
• Traditional methods struggle with non-invertible covariance matrices, limiting their applicability.

Purpose of the Study:

• To develop a novel regularized covariance estimation method.
• To address the critical issue of non-invertible covariance matrices.
• To enhance the numerical stability and reliability of covariance estimation.

Main Methods:

• A novel regularized covariance estimation technique was developed.
• The method was integrated into the analytical solution framework of logistic regression.
• The proposed method was applied to portfolio return management.

Main Results:

• The proposed method ensures the invertibility of the estimated covariance matrix.
• Integration into logistic regression significantly improved analytical solution stability and accuracy.
• The method enhanced the quality of optimization solutions in financial applications.
• Experimental results showed superior performance compared to traditional methods in both logistic regression and portfolio optimization.

Conclusions:

• The novel regularized covariance estimation method effectively overcomes the non-invertibility problem.
• The approach offers enhanced stability and accuracy for logistic regression and portfolio optimization.
• The method demonstrates practical value and robustness in financial applications.