# Algorithms for Learning Graphs in Financial Markets

arXiv: https://arxiv.org/abs/2012.15410 · HTML: https://mlsanity.com/paper/2012.15410/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2020.

## Built on by (most cited first, 15 of 15)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [coVariance Neural Networks](https://mlsanity.com/paper/2205.15856/) (2022)
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- [Spatiotemporal Covariance Neural Networks](https://mlsanity.com/paper/2409.10068/) (2024)
- [Polynomial Graphical Lasso: Learning Edges from Gaussian Graph-Stationary Signals](https://mlsanity.com/paper/2404.02621/) (2024)
- [Sparse Covariance Neural Networks](https://mlsanity.com/paper/2410.01669/) (2024)
- [Fair CoVariance Neural Networks](https://mlsanity.com/paper/2409.08558/) (2024)
- [Adaptive Estimation of Graphical Models under Total Positivity](https://mlsanity.com/paper/2210.15471/) (2022)
- [Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation](https://mlsanity.com/paper/2207.14019/) (2022)
- [Online Network Inference from Graph-Stationary Signals with Hidden Nodes](https://mlsanity.com/paper/2409.08760/) (2024)
- [Precision Neural Networks: Joint Graph And Relational Learning](https://mlsanity.com/paper/2509.14821/) (2025)
- [Clusterpath Gaussian Graphical Modeling](https://mlsanity.com/paper/2407.00644/) (2024)
- [Cramer-Rao Bounds for Laplacian Matrix Estimation](https://mlsanity.com/paper/2504.04576/) (2025)
- [CoVariance Filters and Neural Networks over Hilbert Spaces](https://mlsanity.com/paper/2509.13178/) (2025)
- [Joint Precision Neural Networks: Task-Aware Dependency and Predictive Learning](https://mlsanity.com/paper/2610.06023/) (2026)

## Abstract (arXiv)

In the past two decades, the field of applied finance has tremendously benefited from graph theory. As a result, novel methods ranging from asset network estimation to hierarchical asset selection and portfolio allocation are now part of practitioners' toolboxes. In this paper, we investigate the fundamental problem of learning undirected graphical models under Laplacian structural constraints from the point of view of financial market times series data. In particular, we present natural justifications, supported by empirical evidence, for the usage of the Laplacian matrix as a model for the precision matrix of financial assets, while also establishing a direct link that reveals how Laplacian constraints are coupled to meaningful physical interpretations related to the market index factor and to conditional correlations between stocks. Those interpretations lead to a set of guidelines that practitioners should be aware of when estimating graphs in financial markets. In addition, we design numerical algorithms based on the alternating direction method of multipliers to learn undirected, weighted graphs that take into account stylized facts that are intrinsic to financial data such as heavy tails and modularity. We illustrate how to leverage the learned graphs into practical scenarios such as stock time series clustering and foreign exchange network estimation. The proposed graph learning algorithms outperform the state-of-the-art methods in an extensive set of practical experiments. Furthermore, we obtain theoretical and empirical convergence results for the proposed algorithms. Along with the developed methodologies for graph learning in financial markets, we release an R package, called fingraph, accommodating the code and data to obtain all the experimental results.