# SOFAR: large-scale association network learning

arXiv: https://arxiv.org/abs/1704.08349 · HTML: https://mlsanity.com/paper/1704.08349/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2017.

## Built on by (most cited first, 6 of 6)

- [SOFARI: High-Dimensional Manifold-Based Inference](https://mlsanity.com/paper/2309.15032/) (2023)
- [Parallel integrative learning for large-scale multi-response regression with incomplete outcomes](https://mlsanity.com/paper/2104.05076/) (2021)
- [Simultaneous Heterogeneity and Reduced-rank Learning for Multivariate Response Regression](https://mlsanity.com/paper/2512.06514/) (2025)
- [Simultaneous Best Subset Selection and Dimension Reduction via Primal-Dual Iterations](https://mlsanity.com/paper/2211.15889/) (2022)
- [Row-wise Fusion Regularization: An Interpretable Personalized Federated Learning Framework in Large-Scale Scenarios](https://mlsanity.com/paper/2510.14413/) (2025)
- [LIDS: LLM Summary Inference Under the Layered Lens](https://mlsanity.com/paper/2603.00105/) (2026)

## Abstract (arXiv)

Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsity and orthogonality have been two largely incompatible goals. To accommodate both features, in this paper we suggest the method of sparse orthogonal factor regression (SOFAR) via the sparse singular value decomposition with orthogonality constrained optimization to learn the underlying association networks, with broad applications to both unsupervised and supervised learning tasks such as biclustering with sparse singular value decomposition, sparse principal component analysis, sparse factor analysis, and spare vector autoregression analysis. Exploiting the framework of convexity-assisted nonconvex optimization, we derive nonasymptotic error bounds for the suggested procedure characterizing the theoretical advantages. The statistical guarantees are powered by an efficient SOFAR algorithm with convergence property. Both computational and theoretical advantages of our procedure are demonstrated with several simulation and real data examples.