# CUTS: Neural Causal Discovery from Irregular Time-Series Data

arXiv: https://arxiv.org/abs/2302.07458 · HTML: https://mlsanity.com/paper/2302.07458/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 49 references that are in the map.
- First posted on arXiv 15 Feb 2023.

## Builds on (most cited first, 24 of 24)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [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)
- [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)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)
- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [Neural graphical modelling in continuous-time: consistency guarantees and algorithms](https://mlsanity.com/paper/2105.02522/) (2021)
- [Causal Discovery from Incomplete Data: A Deep Learning Approach](https://mlsanity.com/paper/2001.05343/) (2020)
- [Fast Causal Inference with Non-Random Missingness by Test-Wise Deletion](https://mlsanity.com/paper/1705.09031/) (2017)
- [Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variables](https://mlsanity.com/paper/2102.10324/) (2021)
- [Simultaneous Missing Value Imputation and Structure Learning with Groups](https://mlsanity.com/paper/2110.08223/) (2021)
- [Causal Discovery from Subsampled Time Series Data by Constraint Optimization](https://mlsanity.com/paper/1602.07970/) (2016)
- [The Statistical Recurrent Unit](https://mlsanity.com/paper/1703.00381/) (2017)
- [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)
- [Causal Discovery from Incomplete Data using An Encoder and Reinforcement Learning](https://mlsanity.com/paper/2006.05554/) (2020)
- [Causal Discovery from Sparse Time-Series Data Using Echo State Network](https://mlsanity.com/paper/2201.02933/) (2022)

## Built on by (most cited first, 30 of 33)

- [Mitigating Modality Prior-Induced Hallucinations in Multimodal Large Language Models via Deciphering Attention Causality](https://mlsanity.com/paper/2410.04780/) (2024)
- [CUTS+: High-dimensional Causal Discovery from Irregular Time-series](https://mlsanity.com/paper/2305.05890/) (2023)
- [CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discovery](https://mlsanity.com/paper/2310.01753/) (2023)
- [CausalFormer: An Interpretable Transformer for Temporal Causal Discovery](https://mlsanity.com/paper/2406.16708/) (2024)
- [Neural Structure Learning with Stochastic Differential Equations](https://mlsanity.com/paper/2311.03309/) (2023)
- [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)
- [Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis](https://mlsanity.com/paper/2501.12500/) (2025)
- [Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection](https://mlsanity.com/paper/2506.03964/) (2025)
- [Position: Universal Time Series Foundation Models Rest on a Category Error](https://mlsanity.com/paper/2602.05287/) (2026)
- [CTP:A Causal Interpretable Model for Non-Communicable Disease Progression Prediction](https://mlsanity.com/paper/2308.09735/) (2023)
- [Diffusion model for relational inference](https://mlsanity.com/paper/2401.16755/) (2024)
- [LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Data](https://mlsanity.com/paper/2410.19464/) (2024)
- [Score-matching-based Structure Learning for Temporal Data on Networks](https://mlsanity.com/paper/2412.07469/) (2024)
- [Causal Discovery for Irregularly Time Series with Consistency Guarantees](https://mlsanity.com/paper/2507.03310/) (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)
- [Time Series Domain Adaptation via Latent Invariant Causal Mechanism](https://mlsanity.com/paper/2502.16637/) (2025)
- [Transforming Causality: Transformer-Based Temporal Causal Discovery with Prior Knowledge Integration](https://mlsanity.com/paper/2508.15928/) (2025)
- [Causal Discovery from Time-Series Data with Short-Term Invariance-Based Convolutional Neural Networks](https://mlsanity.com/paper/2408.08023/) (2024)
- [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)
- [Causal-INSIGHT: Probing Temporal Models to Extract Causal Structure](https://mlsanity.com/paper/2603.25473/) (2026)
- [Mask2Cause: Temporal Causal Discovery Beyond Causality in Mean](https://mlsanity.com/paper/2605.07280/) (2026)
- [Time Series Causal Discovery via Context-Conditioned and Causality-Augmented Pretraining](https://mlsanity.com/paper/2605.26759/) (2026)
- [Causal Discovery on Irregular Time Series](https://mlsanity.com/paper/2607.18226/) (2026)
- [AutoCause: A Python framework that automates expert decisions in environmental time-series causal discovery](https://mlsanity.com/paper/2608.00198/) (2026)

## Abstract (arXiv)

Causal discovery from time-series data has been a central task in machine learning. Recently, Granger causality inference is gaining momentum due to its good explainability and high compatibility with emerging deep neural networks. However, most existing methods assume structured input data and degenerate greatly when encountering data with randomly missing entries or non-uniform sampling frequencies, which hampers their applications in real scenarios. To address this issue, here we present CUTS, a neural Granger causal discovery algorithm to jointly impute unobserved data points and build causal graphs, via plugging in two mutually boosting modules in an iterative framework: (i) Latent data prediction stage: designs a Delayed Supervision Graph Neural Network (DSGNN) to hallucinate and register unstructured data which might be of high dimension and with complex distribution; (ii) Causal graph fitting stage: builds a causal adjacency matrix with imputed data under sparse penalty. Experiments show that CUTS effectively infers causal graphs from unstructured time-series data, with significantly superior performance to existing methods. Our approach constitutes a promising step towards applying causal discovery to real applications with non-ideal observations.