Graph learning from data, essential for interpretability and identification of the relationships among data, is a canonical problem that has received substantial attention in the literature. In general, learning a graph with a specific structure is an NP-hard combinatorial problem and thus designing a general tractable algorithm is challenging. Some useful structured graphs include connected, sparse, multi-component, bi-partite, and regular graphs. We focus on the development of efficient algorithms for practical deployment. An open source R package containing the code for all the experiments is available at https://CRAN.R-project.org/package=spectralGraphTopology.
Jiaxi Ying, José Vinícius de M. Cardoso, and Daniel P. Palomar, “Minimax Estimation of Laplacian Constrained Precision Matrices,” in Proc. of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS), vol. 130, pp. 3736-3744, April 2021. [R package]
Jiaxi Ying, José Vinícius de M. Cardoso, and Daniel P. Palomar, “Nonconvex Sparse Graph Learning under Laplacian Constrained Graphical Model,” Advances in Neural Information Processing Systems (NeurIPS), Dec. 2020. [2-min video] [slides] [poster [R package]
Sandeep Kumar, Jiaxi Ying, José Vinícius de M. Cardoso, and Daniel P. Palomar, “A Unified Framework For Structured Graph Learning Via Spectral Constraints,” Journal of Machine Learning Research (JMLR), 21(22): 1-60, Jan. 2020.
Sandeep Kumar, Jiaxi Ying, José Vinícius de M. Cardoso, and Daniel P. Palomar, “Structured Graph Learning Via Laplacian Spectral Constraints,” Advances in Neural Information Processing Systems (NeurIPS), Dec. 2019. [2-min video] [slides] [poster] [arXiv] [R package]
Licheng Zhao, Yiwei Wang, Sandeep Kumar, and Daniel P. Palomar, “Optimization Algorithms for Graph Laplacian Estimation via ADMM and MM,” IEEE Trans. on Signal Processing, vol. 67, no. 16, pp. 4231-4244, Aug. 2019. [R package spectralGraphTopology]