regressiomallin

Regressiomallin is a hypothetical statistical framework that extends standard regression models by introducing a Mallin regularization term to the objective function. The aim is to balance model fit with control of coefficient complexity, allowing simultaneous sparsity and smoothness in the estimated coefficients.

Origin and terminology: The name combines a Latin root for regression with a fictional Mallin penalty, used here to illustrate how alternative regularization schemes can influence model selection and estimation in regression-like settings. It is not associated with any widely recognized real-world method.

Mathematical formulation: For data (X, y), regressiomallin minimizes a loss L(y, Xβ) plus a Mallin penalty P_Mallin(β). The loss can be the least-squares error or a negative log-likelihood, depending on the modeling choice. The Mallin term is designed to be convex under common specifications and can interpolate between or generalize standard penalties, potentially adapting to data structure or predictor relevance.

Computation and properties: Optimization can be performed with proximal gradient methods or coordinate descent when P_Mallin is separable. Under typical regularity conditions, estimators exhibit desirable properties such as consistency and improved generalization in high-dimensional settings, due to the combined emphasis on fit and regularization.

Applications and scope: Regressiomallin is described as suitable for feature selection and prediction in datasets with many predictors, including fields like genomics and social sciences, where controlling model complexity helps prevent overfitting while preserving predictive performance.

See also: regression, regularization, lasso, ridge, elastic net, proximal methods.