# Score-matching-based Structure Learning for Temporal Data on Networks

arXiv: https://arxiv.org/abs/2412.07469 · HTML: https://mlsanity.com/paper/2412.07469/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 65 references that are in the map.
- First posted on arXiv 10 Dec 2024.

## Builds on (most cited first, 25 of 25)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Vision GNN: An Image is Worth Graph of Nodes](https://mlsanity.com/paper/2206.00272/) (2022)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [Ordering-Based Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/2105.06631/) (2021)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Scalable Causal Discovery with Score Matching](https://mlsanity.com/paper/2304.03382/) (2023)
- [Causal Discovery with Score Matching on Additive Models with Arbitrary Noise](https://mlsanity.com/paper/2304.03265/) (2023)
- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [CUTS: Neural Causal Discovery from Irregular Time-Series Data](https://mlsanity.com/paper/2302.07458/) (2023)
- [Estimating the Causal Impact of Recommendation Systems from Observational Data](https://mlsanity.com/paper/1510.05569/) (2015)
- [A Sound and Complete Algorithm for Learning Causal Models from Relational Data](https://mlsanity.com/paper/1309.6843/) (2013)
- [Structure learning of Hamiltonians from real-time evolution](https://mlsanity.com/paper/2405.00082/) (2024)
- [Hessian Estimation via Stein's Identity in Black-Box Problems](https://mlsanity.com/paper/2104.01317/) (2021)
- [Directed Acyclic Graph Structure Learning from Dynamic Graphs](https://mlsanity.com/paper/2211.17029/) (2022)
- [MolNet: A Chemically Intuitive Graph Neural Network for Prediction of Molecular Properties](https://mlsanity.com/paper/2203.09456/) (2022)

## Built on by (most cited first, 2 of 2)

- [Causal Ordering for Structure Learning from Time Series](https://mlsanity.com/paper/2510.24639/) (2025)
- [Intervention-Based Time Series Causal Discovery via Simulator-Generated Interventional Distributions](https://mlsanity.com/paper/2605.09870/) (2026)

## Abstract (arXiv)

Causal discovery is a crucial initial step in establishing causality from empirical data and background knowledge. Numerous algorithms have been developed for this purpose. Among them, the score-matching method has demonstrated superior performance across various evaluation metrics, particularly for the commonly encountered Additive Nonlinear Causal Models. However, current score-matching-based algorithms are primarily designed to analyze independent and identically distributed (i.i.d.) data. More importantly, they suffer from high computational complexity due to the pruning step required for handling dense Directed Acyclic Graphs (DAGs). To enhance the scalability of score matching, we have developed a new parent-finding subroutine for leaf nodes in DAGs, significantly accelerating the most time-consuming part of the process: the pruning step. This improvement results in an efficiency-lifted score matching algorithm, termed Parent Identification-based Causal structure learning for both i.i.d. and temporal data on networKs, or PICK. The new score-matching algorithm extends the scope of existing algorithms and can handle static and temporal data on networks with weak network interference. Our proposed algorithm can efficiently cope with increasingly complex datasets that exhibit spatial and temporal dependencies, commonly encountered in academia and industry. The proposed algorithm can accelerate score-matching-based methods while maintaining high accuracy in real-world applications.