regularfit

Regularfit is a term used to describe a fit produced by a regularization approach in statistics and machine learning. It denotes a model estimation that adds a penalty term to the loss function, constraining the complexity of the model in addition to minimizing the error on the training data. The purpose is to reduce overfitting, improve generalization, and manage multicollinearity, especially in high-dimensional settings where the number of features is large relative to the number of observations.

The method works by minimizing an objective that combines a loss function with a regularization term. Common penalties include L2 regularization (ridge), which shrinks coefficients toward zero without eliminating them; L1 regularization (lasso), which can set some coefficients exactly to zero, producing sparse models; and elastic-net, which blends L1 and L2 penalties. Other penalties target smoothness or group structure, used in specialized models.

Parameter selection: The strength of the penalty is controlled by a regularization parameter, often denoted lambda or alpha. It is typically chosen by cross-validation, information criteria, or domain-specific considerations.

Applications: Regularfit concepts are used across linear and generalized linear models, logistic regression, survival models, and many machine learning methods that include weight decay or penalties. They are especially common in high-dimensional biology, finance, and text data.

Advantages and limitations: Regularized fits reduce variance at the cost of introducing bias, can improve predictive accuracy, and in the case of L1 promote sparse solutions. The choice of penalty and parameter deeply affects model interpretability and performance.

See also: regularization, ridge regression, lasso, elastic net, cross-validation.