fracridge

fracridge implements fractional ridge regression by reparameterizing ridge regression with γ, the ratio between the L2-norms of regularized and unregularized coefficients, to provide interpretable regularization control for high-dimensional data analysis.

Key Features:

• Reparameterization using γ: FRR replaces the traditional hyperparameter α with γ defined as the ratio between the L2-norms of regularized and unregularized coefficients.
• Guaranteed variation in solutions: Solutions obtained for different γ values are guaranteed to vary, preventing redundant calculations across parameter settings.
• Automatic spanning of regularization range: FRR automatically covers the relevant range of regularization without extensive manual exploration.
• Efficiency and scalability: The method includes an algorithm that efficiently implements FRR, making it suitable for large-scale data analysis.
• Interpretability: Framing regularization via γ yields more interpretable and comparable coefficient estimates across models and datasets, beneficial for brain imaging analyses.
• Implementations: Open-source implementations are provided in Python and MATLAB.

Scientific Applications:

• Brain imaging analysis: FRR provides interpretable coefficient estimates and comparable regularization control for complex brain imaging datasets.
• High-dimensional data regularization: FRR addresses hyperparameter selection and interpretability challenges in large, high-dimensional biological datasets.

Methodology:

Reparameterize ridge regression by defining γ as the ratio of L2-norms of regularized and unregularized coefficients and solve for coefficients across γ values; an efficient algorithm implements FRR and ensures solutions vary and span the regularization range.