# Causal Discovery from Conditionally Stationary Time Series

arXiv: https://arxiv.org/abs/2110.06257 · HTML: https://mlsanity.com/paper/2110.06257/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 87 references that are in the map.
- First posted on arXiv 12 Oct 2021.

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [CLEVRER: CoLlision Events for Video REpresentation and Reasoning](https://mlsanity.com/paper/1910.01442/) (2019)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [A Structured Self-attentive Sentence Embedding](https://mlsanity.com/paper/1703.03130/) (2017)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [CATER: A diagnostic dataset for Compositional Actions and TEmporal Reasoning](https://mlsanity.com/paper/1910.04744/) (2019)
- [Counterfactual Generative Networks](https://mlsanity.com/paper/2101.06046/) (2021)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series](https://mlsanity.com/paper/2006.12107/) (2020)
- [Causal Discovery in Physical Systems from Videos](https://mlsanity.com/paper/2007.00631/) (2020)
- [Causal Discovery with General Non-Linear Relationships Using Non-Linear ICA](https://mlsanity.com/paper/1904.09096/) (2019)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models](https://mlsanity.com/paper/1905.10857/) (2019)
- [Reconstructing regime-dependent causal relationships from observational time series](https://mlsanity.com/paper/2007.00267/) (2020)
- [Multiple Causal Inference with Latent Confounding](https://mlsanity.com/paper/1805.08273/) (2018)
- [Neural Relational Inference with Efficient Message Passing Mechanisms](https://mlsanity.com/paper/2101.09486/) (2021)
- [Causal Discovery in the Presence of Measurement Error: Identifiability Conditions](https://mlsanity.com/paper/1706.03768/) (2017)

## Built on by (most cited first, 12 of 12)

- [Case Studies of Causal Discovery from IT Monitoring Time Series](https://mlsanity.com/paper/2307.15678/) (2023)
- [Evaluating Temporal Observation-Based Causal Discovery Techniques Applied to Road Driver Behaviour](https://mlsanity.com/paper/2302.00064/) (2023)
- [TS-CausalNN: Learning Temporal Causal Relations from Non-linear Non-stationary Time Series Data](https://mlsanity.com/paper/2404.01466/) (2024)
- [Generating Hypotheses of Dynamic Causal Graphs in Neuroscience: Leveraging Generative Factor Models of Observed Time Series](https://mlsanity.com/paper/2505.20697/) (2025)
- [End-to-End Identifiable and Consistent Recurrent Switching Dynamical Systems](https://mlsanity.com/paper/2605.06315/) (2026)
- [Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families](https://mlsanity.com/paper/2606.02231/) (2026)
- [GDBN: a Graph Neural Network Approach to Dynamic Bayesian Network](https://mlsanity.com/paper/2302.10804/) (2023)
- [Distributed Dynamic Invariant Causal Prediction in Environmental Time Series](https://mlsanity.com/paper/2603.02902/) (2026)
- [TTCD:Transformer Integrated Temporal Causal Discovery from Non-Stationary Time Series Data](https://mlsanity.com/paper/2605.08111/) (2026)
- [Hierarchical Causal Abduction: A Foundation Framework for Explainable Model Predictive Control](https://mlsanity.com/paper/2605.10624/) (2026)
- [Symmetries and Causality: Causal Effect Identification Beyond IID Data](https://mlsanity.com/paper/2609.03697/) (2026)
- [Beyond Stationarity in Time Series: Discovering Causal Structures and Latent Regimes via Markov Blankets](https://mlsanity.com/paper/2609.05150/) (2026)

## Abstract (arXiv)

Causal discovery, i.e., inferring underlying causal relationships from observational data, is highly challenging for AI systems. In a time series modeling context, traditional causal discovery methods mainly consider constrained scenarios with fully observed variables and/or data from stationary time-series. We develop a causal discovery approach to handle a wide class of nonstationary time series that are conditionally stationary, where the nonstationary behaviour is modeled as stationarity conditioned on a set of latent state variables. Named State-Dependent Causal Inference (SDCI), our approach is able to recover the underlying causal dependencies, with provable identifiablity for the state-dependent causal structures. Empirical experiments on nonlinear particle interaction data and gene regulatory networks demonstrate SDCI's superior performance over baseline causal discovery methods. Improved results over non-causal RNNs on modeling NBA player movements demonstrate the potential of our method and motivate the use of causality-driven methods for forecasting.