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mdpeer

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.

1. riPEERc (ridgified Partially Empirical Eigenvectors for Regression with constant) method utilizes additional Ridge term to handle the non-invertibility of a graph Laplacian matrix.

2. vrPEER (variable reducted PEER) method performs variable-reduction procedure to handle the non-invertibility of a graph Laplacian matrix.

3. 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.