A nearly-linear time framework for graph-structured sparsity

We introduce a framework for sparsity structures defined via graphs. Our approach is flexible and generalizes several previously studied sparsity models. Moreover, we provide efficient projection algorithms for our sparsity model that run in nearly-linear time. In the context of sparse recovery, our framework achieves an informationtheoretically optimal sample complexity for a wide range of parameters. We complement our theoretical analysis with experiments showing that our algorithms also improve on prior work in practice.