seagull

seagull implements lasso, group lasso, and sparse-group lasso regularization for high-dimensional linear models (including mixed models with fixed and random effects) using proximal gradient descent to enable variable selection and mitigate multicollinearity.

Key Features:

• Lasso (Least Absolute Shrinkage and Selection Operator): Performs L1 regularization for sparse variable selection in linear models.
• Group Lasso: Applies grouped-variable selection to include or exclude predefined variable groups jointly.
• Sparse-Group Lasso: Combines L1 and group penalties with a mixing parameter (0 ≤ α ≤ 1) to enable simultaneous selection of individual variables and groups.
• Proximal Gradient Descent: Solves the regularized optimization problems using proximal gradient methods.
• Backtracking Line Search: Determines step sizes during proximal gradient iterations to ensure stable convergence.
• Warm Starts: Uses solutions from previous penalty values as initializations during grid searches over penalty parameters.
• Mixed Models Support: Handles models with fixed and random effects within the linear modeling framework.
• Regularization Paths: Computes complete regularization paths across penalty parameters for model exploration.
• Grouped Input Requirement: Expects pre-defined grouping or clustering of predictors for group lasso and sparse-group lasso applications.

Scientific Applications:

• Variable Selection in High-Dimensional Data: Identifies relevant predictors from datasets with more explanatory variables than observations.
• Multicollinearity Mitigation: Reduces effects of correlated predictors common in life-science datasets.
• Group-Wise Inference: Enables selection and interpretation of biologically meaningful groups of predictors.
• Model Tuning and Exploration: Facilitates exploration of model behavior across penalty parameters via regularization paths.

Methodology:

Optimization is performed with proximal gradient descent using backtracking line search for step-size selection and warm starts for grid searches over penalty parameters.