Stochastic Variance-Reduced Iterative Hard Thresholding in Graph Sparsity Optimization

• URL: http://arxiv.org/abs/2407.16968v1
• Date: Wed, 24 Jul 2024 03:26:26 GMT
• Title: Stochastic Variance-Reduced Iterative Hard Thresholding in Graph Sparsity Optimization
• Authors: Derek Fox, Samuel Hernandez, Qianqian Tong,
• Abstract summary: We introduce two methods to solve gradient-based graph sparsity optimization: GraphRG-IHT and GraphSG-IHT. We provide a general general for theoretical analysis, demonstrating that methods enjoy a gradient-based framework.
• Score: 0.626226809683956
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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

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