  The bootstrap algebraic multigrid framework allows for the adaptive
construction of algebraic multigrid methods in situations where geometric
multigrid methods are not known or not available at all. While there has been
some work on adaptive coarsening in this framework in terms of algebraic
distances, coarsening is the part of the adaptive bootstrap setup that is least
developed. In this paper we try to close this gap by introducing an adaptive
coarsening scheme that views interpolation as a local regression problem. In
fact the bootstrap algebraic multigrid setup can be understood as a machine
learning ansatz that learns the nature of smooth error by local regression. In
order to turn this idea into a practical method we modify least squares
interpolation to both avoid overfitting of the data and to recover a sparse
response that can be used to extract information about the coupling strength
amongst variables like in classical algebraic multigrid. In order to improve
the so-found coarse grid we propose a post-processing to ensure stability of
the resulting least squares interpolation operator. We conclude with numerical
experiments that show the viability of the chosen approach.
