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Updated: Jan 26, 2026

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Greedy Projected Gradient-Newton Method for Sparse Logistic Regression.

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    We introduce a new greedy projected gradient-Newton (GPGN) method for sparse logistic regression (SLR). This method offers theoretical convergence guarantees and demonstrates superior speed and accuracy in numerical experiments for classification and feature selection.

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    Area of Science:

    • Machine Learning
    • Statistical Modeling

    Background:

    • Sparse logistic regression (SLR) is crucial for classification and feature selection in fields like deep learning and bioinformatics.
    • Classical SLR models incorporate sparsity constraints into logistic regression.

    Purpose of the Study:

    • To theoretically analyze the existence and uniqueness of solutions for SLR.
    • To propose and evaluate a novel greedy projected gradient-Newton (GPGN) method for solving SLR problems.

    Main Methods:

    • The proposed GPGN method combines projected gradient and Newton methods.
    • Theoretical analysis was conducted on the convergence properties of the GPGN method.
    • Numerical experiments were performed to compare GPGN with state-of-the-art solvers.

    Main Results:

    • The GPGN method guarantees convergence to a global/local minimizer under weaker conditions.
    • The method exhibits finite identification of the optimal support set and local quadratic convergence.
    • Numerical results show GPGN achieves higher accuracy and speed compared to existing solvers.

    Conclusions:

    • The GPGN method provides elegant theoretical results and remarkable numerical performance for SLR.
    • It offers an efficient and accurate approach for classification and feature selection tasks.
    • This work advances the practical application of sparse logistic regression in various scientific domains.