# Stochastic Iterative Hard Thresholding for Graph-structured Sparsity Optimization

arXiv: https://arxiv.org/abs/1905.03652 · HTML: https://mlsanity.com/paper/1905.03652/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2019.

## Built on by (most cited first, 3 of 3)

- [Statistically-Robust Clustering Techniques for Mapping Spatial Hotspots: A Survey](https://mlsanity.com/paper/2103.12019/) (2021)
- [Stochastic Variance-Reduced Iterative Hard Thresholding in Graph Sparsity Optimization](https://mlsanity.com/paper/2407.16968/) (2024)
- [Probabilistic Iterative Hard Thresholding for Sparse Learning](https://mlsanity.com/paper/2409.01413/) (2024)

## Abstract (arXiv)

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity information is very specific, e.g., convex sparsity-inducing norms or ℓ0-norm. However, these norms cannot be directly applied to the problem of complex (non-convex) graph-structured sparsity models, which have important application in disease outbreak and social networks, etc. In this paper, we propose a stochastic gradient-based method for solving graph-structured sparsity constraint problems, not restricted to the least square loss. We prove that our algorithm enjoys a linear convergence up to a constant error, which is competitive with the counterparts in the batch learning setting. We conduct extensive experiments to show the efficiency and effectiveness of the proposed algorithms.