  Stochastic optimization algorithms are widely used for large-scale data
analysis due to their low per-iteration costs, but they often suffer from slow
asymptotic convergence caused by inherent variance. Variance-reduced techniques
have been therefore used to address this issue in structured sparse models
utilizing sparsity-inducing norms or $\ell_0$-norms. However, these techniques
are not directly applicable to complex (non-convex) graph sparsity models,
which are essential in applications like disease outbreak monitoring and social
network analysis. In this paper, we introduce two stochastic variance-reduced
gradient-based methods to solve graph sparsity optimization: GraphSVRG-IHT and
GraphSCSG-IHT. We provide a general framework for theoretical analysis,
demonstrating that our methods enjoy a linear convergence speed. Extensive
experiments validate
