This repository contains R code that implements a block-structured regularization for regression problems with network-valued covariates to perform supervised community detection and regularized regression simultaneously (see the arxiv manuscript Arroyo and Levina (2019)).
Given a sample of N pairs of networks with aligned vertices (represented with their
adjacency matrices) and responses
, where
is a real-valued variable, the method fits a regression model to predict
using a linear combination of the entries of
. A matrix
encodes the coefficients of the linear model to form a prediction rule of the form
,
To enforce regularization and structure in the coefficients, the methods imposes a block-structured constraint by dividing the rows and columns of into
different groups. This is analogous to the community detection problem, and by fitting a regularization of this form, the method can cluster the nodes of the networks into "supervised communities". Additionally, this constraint effectively reduces the number of different coefficients to deal with the high-dimensionality of the problem.
The constraint has the form , where
is a matrix with its rows indicating the community memberships for each node, and
is a matrix of coefficients.
Arroyo, J. and Levina, E. "Simultaneous prediction and community detection for networks with application to neuroimaging"
