# Dynamic Causal Structure Discovery and Causal Effect Estimation

arXiv: https://arxiv.org/abs/2501.06534 · HTML: https://mlsanity.com/paper/2501.06534/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 45 references that are in the map.
- First posted on arXiv 11 Jan 2025.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [Causal Structure Learning](https://mlsanity.com/paper/1706.09141/) (2017)
- [A Transformational Characterization of Equivalent Bayesian Network Structures](https://mlsanity.com/paper/1302.4938/) (2013)
- [Assessing Time-Varying Causal Effect Moderation in Mobile Health](https://mlsanity.com/paper/1601.00237/) (2016)
- [Directed Acyclic Graph Structure Learning from Dynamic Graphs](https://mlsanity.com/paper/2211.17029/) (2022)

## Built on by (most cited first, 3 of 3)

- [PrAda-GAN: A Private Adaptive Generative Adversarial Network with Bayes Network Structure](https://mlsanity.com/paper/2511.07997/) (2025)
- [M-learner:A Flexible And Powerful Framework To Study Heterogeneous Treatment Effect In Mediation Model](https://mlsanity.com/paper/2505.17917/) (2025)
- [DDT: A Dual-Masking Dual-Expert Transformer for Energy Time-Series Forecasting](https://mlsanity.com/paper/2601.07250/) (2026)

## Abstract (arXiv)

To represent the causal relationships between variables, a directed acyclic graph (DAG) is widely utilized in many areas, such as social sciences, epidemics, and genetics. Many causal structure learning approaches are developed to learn the hidden causal structure utilizing deep-learning approaches. However, these approaches have a hidden assumption that the causal relationship remains unchanged over time, which may not hold in real life. In this paper, we develop a new framework to model the dynamic causal graph where the causal relations are allowed to be time-varying. We incorporate the basis approximation method into the score-based causal discovery approach to capture the dynamic pattern of the causal graphs. Utilizing the autoregressive model structure, we could capture both contemporaneous and time-lagged causal relationships while allowing them to vary with time. We propose an algorithm that could provide both past-time estimates and future-time predictions on the causal graphs, and conduct simulations to demonstrate the usefulness of the proposed method. We also apply the proposed method for the covid-data analysis, and provide causal estimates on how policy restriction's effect changes.