An effective method for modeling highly correlated interaction models with applications in Alzheimer's...

Interactions and correlations among features are essential in biology, as well as in other fields. This article introduces a novel approach for linear interaction models characterized by complex correlation structures. By integrating local linear approximation and Laplacian smoothing penalty with $l_1$ or $l_1$ and $l_2$ penalties, our methods effectively estimate and predict highly correlated interaction models. Theoretical analysis confirms that both methods converge to an oracle solution within two iterations, demonstrating a rapid convergence rate. In simulation studies, our proposed methods outperform existing techniques in terms of prediction accuracy, estimation precision, and variable selection. When applied to protein microarray data for Alzheimer's disease analysis, they reveal substantial main and interaction effects with notably lower prediction errors. This highlights the potential of our methods as powerful tools for analyzing linear interaction models with intricate correlations, applicable across a wide range of biological research and other fields.