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.