Maximal Associated Regression: A Nonlinear Extension to Least Angle Regression

This paper proposes Maximal Associated Regression (MAR), a novel algorithm that performs forward stage-wise regression by applying nonlinear transformations to fit predictor covariates. For each predictor, MAR selects between linear or additive as determined the dataset. The proposed is an adaptation of Least Angle (LARS) and retains its efficiency in building sparse models. Constrained penalized splines are used generate smooth for fits. A monotonically constrained extension (MARm) also introduced this isotonic problems. algorithms validated on both synthetic real datasets. performances MARm compared against LARS, Generalized Linear Models (GLM), Additive (GAM) under Gaussian assumption with unity link function. Results indicate MAR-type achieve superior subset selection accuracy, generating sparser models generalize well new data. able sample deficient Thus, valuable tool data exploration, especially when priori knowledge dataset unavailable.