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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.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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