Provides graph-constrained regression methods in which regularization parameters are selected automatically via estimation of equivalent Linear Mixed Model formulation. 'riPEER' (ridgified Partially Empirical Eigenvectors for Regression) method employs a penalty term being a linear combination of graph-originated and ridge-originated penalty terms, whose two regularization parameters are ML estimators from corresponding Linear Mixed Model solution; a graph-originated penalty term allows imposing similarity between coefficients based on graph information given whereas additional ridge-originated penalty term facilitates parameters estimation: it reduces computational issues arising from singularity in a graph-originated penalty matrix and yields plausible results in situations when graph information is not informative. 'riPEERc' (ridgified Partially Empirical Eigenvectors for Regression with constant) method utilizes addition of a diagonal matrix multiplied by a predefined (small) scalar to handle the non-invertibility of a graph Laplacian matrix. 'vrPEER' (variable reducted PEER) method performs variable-reduction procedure to handle the non-invertibility of a graph Laplacian matrix.
Graph-Constrained Regression with Enhanced Regularization Parameters
Performs graph-constrained regularization in which regularization parameters are selected with the use of a known fact of equivalence between penalized regression and Linear Mixed Model solutions. Provides implementation of three regression methods where graph-constraints among coefficients are accounted for.
riPEERc
(ridgified Partially Empirical Eigenvectors for Regression with constant) method utilizes additional Ridge term to handle the non-invertibility of a graph Laplacian matrix.
vrPEER
(variable reducted PEER) method performs variable-reduction procedure to handle the non-invertibility of a graph Laplacian matrix.
riPEER
(ridgified Partially Empirical Eigenvectors for Regression) method employs a penalty term being a linear combination of graph-originated and ridge-originated penalty terms, whose two regularization parameters are ML estimators from corresponding Linear Mixed Model solution.
Notably, in riPEER
method a graph-originated penalty term allows imposing similarity between coefficients based on graph information given whereas additional ridge-originated penalty term facilitates parameters estimation: it reduces computational issues arising from singularity in a graph- originated penalty matrix and yields plausible results in situations when graph information is not informative or when it is unclear whether connectivities represented by a graph reflect similarities among corresponding coefficients.