# Causal Discovery for Irregularly Time Series with Consistency Guarantees

arXiv: https://arxiv.org/abs/2507.03310 · HTML: https://mlsanity.com/paper/2507.03310/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 61 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Builds on (most cited first, 30 of 33)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Generalization Properties of Learning with Random Features](https://mlsanity.com/paper/1602.04474/) (2016)
- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Causal Machine Learning for Healthcare and Precision Medicine](https://mlsanity.com/paper/2205.11402/) (2022)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Causal Discovery with Score Matching on Additive Models with Arbitrary Noise](https://mlsanity.com/paper/2304.03265/) (2023)
- [Neural graphical modelling in continuous-time: consistency guarantees and algorithms](https://mlsanity.com/paper/2105.02522/) (2021)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [CUTS+: High-dimensional Causal Discovery from Irregular Time-series](https://mlsanity.com/paper/2305.05890/) (2023)
- [Learning from Irregularly-Sampled Time Series: A Missing Data Perspective](https://mlsanity.com/paper/2008.07599/) (2020)
- [CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discovery](https://mlsanity.com/paper/2310.01753/) (2023)
- [NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge](https://mlsanity.com/paper/2109.04286/) (2021)
- [CUTS: Neural Causal Discovery from Irregular Time-Series Data](https://mlsanity.com/paper/2302.07458/) (2023)
- [Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noise](https://mlsanity.com/paper/2210.14706/) (2022)
- [A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Models](https://mlsanity.com/paper/2303.18211/) (2023)
- [Causal Discovery from Incomplete Data: A Deep Learning Approach](https://mlsanity.com/paper/2001.05343/) (2020)
- [CausalRivers -- Scaling up benchmarking of causal discovery for real-world time-series](https://mlsanity.com/paper/2503.17452/) (2025)
- [MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models](https://mlsanity.com/paper/2205.13869/) (2022)
- [Identification In Missing Data Models Represented By Directed Acyclic Graphs](https://mlsanity.com/paper/1907.00241/) (2019)
- [Entropy-based Discovery of Summary Causal Graphs in Time Series](https://mlsanity.com/paper/2105.10381/) (2021)
- [Causal Discovery from Subsampled Time Series with Proxy Variables](https://mlsanity.com/paper/2305.05276/) (2023)
- [Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discovery](https://mlsanity.com/paper/2503.17037/) (2025)
- [Learning Instrumental Variable from Data Fusion for Treatment Effect Estimation](https://mlsanity.com/paper/2208.10912/) (2022)
- [Identification of Causal Structure in the Presence of Missing Data with Additive Noise Model](https://mlsanity.com/paper/2312.12206/) (2023)

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

- [Benchmarking Sensor-Fault Robustness in Forecasting](https://mlsanity.com/paper/2605.10822/) (2026)
- [ITSY: Causal Discovery From Irregular Time-Series Data](https://mlsanity.com/paper/2609.23516/) (2026)

## Abstract (arXiv)

This paper studies causal discovery in irregularly sampled time series-a key challenge in risk-sensitive domains like finance, healthcare, and climate science, where missing data and inconsistent sampling frequencies distort causal mechanisms. The main challenge comes from the interdependence between missing data imputation and causal structure recovery: errors in imputation and structure learning can reinforce each other, leading to an inaccurate causal graph. Existing methods either impute first and then discover, or jointly optimize both via neural representation learning, but lack explicit mechanisms to ensure mutual consistency of imputation and structure learning. We address this challenge with ReTimeCausal, an EM-based framework that alternates between imputation and structure learning, which encourages structural consistency throughout the optimization process. Our framework provides theoretical consistency guarantees for structure recovery and extends classical results to settings with irregular sampling and high missingness. ReTimeCausal combines kernel-based sparse regression and structural constraints in an alternating process that updates the completed data and the causal graph in turn. Experiments on synthetic and real-world datasets show that ReTimeCausal is more effective than existing methods under challenging irregular sampling and missing data.