Graph Learning in Finance

Financial markets are inherently interconnected systems where assets, institutions, and market participants form complex networks of relationships that evolve over time. Graph learning has emerged as a powerful framework for understanding and modeling these financial networks, enabling the discovery of meaningful relationships among stocks, cryptocurrencies, or other financial instruments through their return time series, trading volumes, or other market indicators. By representing financial data as nodes in a graph and learning the edge weights that capture dependencies and spillover effects, graph learning techniques can reveal market sectors, risk propagation channels, and trading communities that may not be apparent from traditional financial analysis. This network perspective is particularly valuable for portfolio optimization, systemic risk assessment, and market surveillance, where understanding the underlying structure of financial relationships can lead to more robust investment strategies and better risk management practices.

Software

GitHub software webpage

• spectralGraphTopology: Structured graph learning via Laplacian spectral constraints (NeurIPS 2019) [CRAN]
• sparseGraph: Nonconvex Sparse Graph Learning under Laplacian-structured Graphical Model (NeurIPS 2020)
• fingraph: Graphical Models in Heavy-Tailed Markets (NeurIPS 2021) [CRAN]
• bipartite: Learning Bipartite Graphs: Heavy Tails and Multiple Components (NeurIPS 2022) [CRAN]

Book chapters

• José Vinícius de M. Cardoso, Jiaxi Ying, and Daniel P. Palomar, “Learning Graphs from Heavy-Tailed Data,” in Elliptically Symmetric Distributions in Signal Processing and Machine Learning, Eds. J.-P. Delmas, M. N. El Korso, S. Fortunati, F. Pascal, Springer, Jul. 2024.

• José Vinícius de M. Cardoso, Jiaxi Ying, and Daniel P. Palomar, “Nonconvex Graph Learning: Sparsity, Heavy-tails, and Clustering,” in Signal Processing and Machine Learning Theory, Digital Signal Processing Series, Elsevier, Dec. 2022. 📕

Papers

• Amirhossein Javaheri, Arash Amini, Farokh Marvasti, and Daniel P. Palomar, “Learning Spatio-Temporal Graphical Models From Incomplete Observations,” IEEE Trans. on Signal Processing, vol. 72, pp. 1361-1374, 2024.

• Jian-Feng Cai, José Vinícius de M. Cardoso, Daniel P. Palomar, and Jiaxi Ying, “Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity,” Advances in Neural Information Processing Systems (NeurIPS), New Orleans, LA, USA, Dec. 2023. [26.1% acceptance rate] [video] [slides] [poster]

• Xiwen Wang, Jiaxi Ying, and Daniel P. Palomar, “Learning Large-Scale MTP2 Gaussian Graphical Models via Bridge-Block Decomposition,” Advances in Neural Information Processing Systems (NeurIPS), New Orleans, LA, USA, Dec. 2023. [26.1% acceptance rate] [video] [slides] [poster]

• Jiaxi Ying, José Vinícius de M. Cardoso, and Daniel P. Palomar, “Adaptive Estimation of Graphical Models under Total Positivity,” in Proc. of the International Conference on Machine Learning (ICML), Honolulu, HI, USA, July 2023. [27.9% acceptance rate]

• José Vinícius de M. Cardoso, Jiaxi Ying, and Daniel P. Palomar, “Learning Bipartite Graphs: Heavy Tails and Multiple Components,” Advances in Neural Information Processing Systems (NeurIPS), New Orleans, LA, USA, Dec. 2022. [25.6% acceptance rate] [video] [slides] [poster] [R package bipartite]

• Rui Zhou, Jiaxi Ying, and Daniel P. Palomar, “Covariance Matrix Estimation Under Low-Rank Factor Model with Nonnegative Correlations,” IEEE Trans. on Signal Processing, vol. 70, pp. 4020-4030, Aug. 2022.

• José Vinícius de M. Cardoso, Jiaxi Ying, and Daniel P. Palomar, “Graphical Models for Heavy-Tailed Markets,” Advances in Neural Information Processing Systems (NeurIPS), Virtual, Dec. 2021. [26% acceptance rate] [video] [supplemental material] [slides] [poster] [R package fingraph]

• 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. [29.8% acceptance rate] [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]