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, we show that our framework achieves an information-theoretically optimal sample complexity for a wide range of parameters. We complement our theoretical analysis with experiments demonstrating that our algorithms also improve on prior work in practice.