# CUTS+: High-dimensional Causal Discovery from Irregular Time-series

arXiv: https://arxiv.org/abs/2305.05890 · HTML: https://mlsanity.com/paper/2305.05890/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 57 references that are in the map.
- First posted on arXiv 10 May 2023.

## Builds on (most cited first, 26 of 26)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [From Coarse to Fine: Robust Hierarchical Localization at Large Scale](https://mlsanity.com/paper/1812.03506/) (2018)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [High-recall causal discovery for autocorrelated time series with latent confounders](https://mlsanity.com/paper/2007.01884/) (2020)
- [Modeling Missing Data in Clinical Time Series with RNNs](https://mlsanity.com/paper/1606.04130/) (2016)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Neural graphical modelling in continuous-time: consistency guarantees and algorithms](https://mlsanity.com/paper/2105.02522/) (2021)
- [CUTS: Neural Causal Discovery from Irregular Time-Series Data](https://mlsanity.com/paper/2302.07458/) (2023)
- [Simultaneous Missing Value Imputation and Structure Learning with Groups](https://mlsanity.com/paper/2110.08223/) (2021)
- [Granger causal inference on DAGs identifies genomic loci regulating transcription](https://mlsanity.com/paper/2210.10168/) (2022)
- [Complete Inference of Causal Relations between Dynamical Systems](https://mlsanity.com/paper/1808.10806/) (2018)
- [Hankel low-rank approximation and completion in time series analysis and forecasting: a brief review](https://mlsanity.com/paper/2206.05103/) (2022)

## Built on by (most cited first, 30 of 41)

- [CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discovery](https://mlsanity.com/paper/2310.01753/) (2023)
- [Dynamic Causal Explanation Based Diffusion-Variational Graph Neural Network for Spatio-temporal Forecasting](https://mlsanity.com/paper/2305.09703/) (2023)
- [On the Identification of Temporally Causal Representation with Instantaneous Dependence](https://mlsanity.com/paper/2405.15325/) (2024)
- [Jacobian Regularizer-based Neural Granger Causality](https://mlsanity.com/paper/2405.08779/) (2024)
- [CausalDynamics: A large-scale benchmark for structural discovery of dynamical causal models](https://mlsanity.com/paper/2505.16620/) (2025)
- [Entropy Causal Graphs for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2312.09478/) (2023)
- [Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection](https://mlsanity.com/paper/2506.03964/) (2025)
- [Learning Flexible Time-windowed Granger Causality Integrating Heterogeneous Interventional Time Series Data](https://mlsanity.com/paper/2406.10419/) (2024)
- [DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series](https://mlsanity.com/paper/2511.02137/) (2025)
- [Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studies](https://mlsanity.com/paper/2312.16815/) (2023)
- [OCDB: Revisiting Causal Discovery with a Comprehensive Benchmark and Evaluation Framework](https://mlsanity.com/paper/2406.04598/) (2024)
- [LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Data](https://mlsanity.com/paper/2410.19464/) (2024)
- [Causal Discovery for Irregularly Time Series with Consistency Guarantees](https://mlsanity.com/paper/2507.03310/) (2025)
- [UnCLe: Towards Scalable Dynamic Causal Discovery in Non-linear Temporal Systems](https://mlsanity.com/paper/2511.03168/) (2025)
- [Coarse-to-Fine Learning of Dynamic Causal Structures](https://mlsanity.com/paper/2602.22532/) (2026)
- [Bayesian Vector AutoRegression with Factorised Granger-Causal Graphs](https://mlsanity.com/paper/2402.03614/) (2024)
- [Discovering Latent Causal Graphs from Spatiotemporal Data](https://mlsanity.com/paper/2411.05331/) (2024)
- [Exploring Neural Granger Causality with xLSTMs: Unveiling Temporal Dependencies in Complex Data](https://mlsanity.com/paper/2502.09981/) (2025)
- [Time Series Domain Adaptation via Latent Invariant Causal Mechanism](https://mlsanity.com/paper/2502.16637/) (2025)
- [PropLLM: Propagation-Aware Scene Reconstruction for Network Fault Diagnosis](https://mlsanity.com/paper/2606.00582/) (2026)
- [GRACE: Gated Refinement for Accurate Causal Edge Discovery in High-Dimensional Time Series](https://mlsanity.com/paper/2606.23880/) (2026)
- [CEDAR: Causal Edge Discovery for Autoregressive Processes](https://mlsanity.com/paper/2607.20696/) (2026)
- [Causal Discovery from Time-Series Data with Short-Term Invariance-Based Convolutional Neural Networks](https://mlsanity.com/paper/2408.08023/) (2024)
- [SpinSVAR: Estimating Structural Vector Autoregression Assuming Sparse Input](https://mlsanity.com/paper/2501.03130/) (2025)
- [Causally-informed Deep Learning towards Explainable and Generalizable Outcomes Prediction in Critical Care](https://mlsanity.com/paper/2502.02109/) (2025)
- [Emergent Granger Causality in Neural Networks: Can Prediction Alone Reveal Structure?](https://mlsanity.com/paper/2506.20347/) (2025)
- [A Gradient-based Causal Discovery Framework with Applications to Complex Industrial Processes](https://mlsanity.com/paper/2507.11178/) (2025)
- [Learning Granger Causality under Latent Confounding via Intervention-Induced Heterogeneity](https://mlsanity.com/paper/2510.19138/) (2025)
- [KarmaTS: A Universal Simulation Platform for Multivariate Time Series with Functional Causal Dynamics](https://mlsanity.com/paper/2511.11357/) (2025)
- [A Self-explainable Model of Long Time Series by Extracting Informative Structured Causal Patterns](https://mlsanity.com/paper/2512.01412/) (2025)

## Abstract (arXiv)

Causal discovery in time-series is a fundamental problem in the machine learning community, enabling causal reasoning and decision-making in complex scenarios. Recently, researchers successfully discover causality by combining neural networks with Granger causality, but their performances degrade largely when encountering high-dimensional data because of the highly redundant network design and huge causal graphs. Moreover, the missing entries in the observations further hamper the causal structural learning. To overcome these limitations, We propose CUTS+, which is built on the Granger-causality-based causal discovery method CUTS and raises the scalability by introducing a technique called Coarse-to-fine-discovery (C2FD) and leveraging a message-passing-based graph neural network (MPGNN). Compared to previous methods on simulated, quasi-real, and real datasets, we show that CUTS+ largely improves the causal discovery performance on high-dimensional data with different types of irregular sampling.