mlsanityData to 7 Oct 2026

Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noise

arXiv 2210.14706 ↗First posted 26 Oct 2022cs.LG cs.AI stat.MLcited by 30

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Abstract (arXiv)

Discovering causal relationships between different variables from time series data has been a long-standing challenge for many domains such as climate science, finance, and healthcare. Given the complexity of real-world relationships and the nature of observations in discrete time, causal discovery methods need to consider non-linear relations between variables, instantaneous effects and history-dependent noise (the change of noise distribution due to past actions). However, previous works do not offer a solution addressing all these problems together. In this paper, we propose a novel causal relationship learning framework for time-series data, called Rhino, which combines vector auto-regression, deep learning and variational inference to model non-linear relationships with instantaneous effects while allowing the noise distribution to be modulated by historical observations. Theoretically, we prove the structural identifiability of Rhino. Our empirical results from extensive synthetic experiments and two real-world benchmarks demonstrate better discovery performance compared to relevant baselines, with ablation studies revealing its robustness under model misspecification.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). Builds on 25 of its 53 references that are in the map. First posted on arXiv 26 Oct 2022.

Builds on

25 of 53 references.

References · 25

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13 more
  1. 2020Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Datacited by 99
  2. 2020Causal Autoregressive Flowscited by 97
  3. 2022Deep End-to-end Causal Inferencecited by 93
  4. 2019Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causalitycited by 55
  5. 2018Conditional Density Estimation with Bayesian Normalising Flowscited by 54
  6. 2021Causal Inference for Time series Analysis: Problems, Methods and Evaluationcited by 42
  7. 2020Invertible Generative Modeling using Linear Rational Splinescited by 39
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 8; 2024: 7; 2025: 6; 2026: 7.

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  1. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  2. 2024Mitigating Modality Prior-Induced Hallucinations in Multimodal Large Language Models via Deciphering Attention Causalitycited by 42
  3. 2023CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discoverycited by 35
  4. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  5. 2023Neural Structure Learning with Stochastic Differential Equationscited by 14
  6. 2022Deep Causal Learning: Representation, Discovery and Inferencecited by 11
  7. 2023Discovering Mixtures of Structural Causal Models from Time Series Datacited by 10
  8. 2023On the Identifiability of Switching Dynamical Systemscited by 9
  9. 2024Jacobian Regularizer-based Neural Granger Causalitycited by 9
  10. 2025Learning General Causal Structures with Hidden Dynamic Process for Climate Analysiscited by 6
  11. 2025ClimateBench-M: A Multi-Modal Climate Data Benchmark with a Simple Generative Methodcited by 4
  12. 2023Double Machine Learning Based Structure Identification from Temporal Datacited by 3
18 more
  1. 2023Causal Temporal Regime Structure Learningcited by 2
  2. 2024LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Datacited by 2
  3. 2024CausalStock: Deep End-to-end Causal Discovery for News-driven Stock Movement Predictioncited by 2
  4. 2025Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noisescited by 2
  5. 2022Identifying Unique Spatial-Temporal Bayesian Network without Markov Equivalencecited by 1
  6. 2024Bayesian Vector AutoRegression with Factorised Granger-Causal Graphscited by 1
  7. 2024Identifying Nonstationary Causal Structures with High-Order Markov Switching Modelscited by 1
  8. 2024Discovering Latent Causal Graphs from Spatiotemporal Datacited by 1
  9. 2025Causal Discovery for Irregularly Time Series with Consistency Guaranteescited by 1
  10. 2026The Failures of Marginal Influence-Based Attribution Methods for Global Time Series Explanationscited by 1
  11. 2025SpinSVAR: Estimating Structural Vector Autoregression Assuming Sparse Inputcited by 0
  12. 2025Robust Causal Discovery in Real-World Time Series with Power-Lawscited by 0
  13. 2026PRCD-MAP: Learning How Much to Trust Imperfect Priors in Causal Discoverycited by 0
  14. 2026Mask2Cause: Temporal Causal Discovery Beyond Causality in Meancited by 0
  15. 2026Time Series Causal Discovery via Context-Conditioned and Causality-Augmented Pretrainingcited by 0
  16. 2026Identifiable Markov Switching Models with Instantaneous Effects and Exponential Familiescited by 0
  17. 2026ITSY: Causal Discovery From Irregular Time-Series Datacited by 0
  18. 2026seq2cause: One Autoregressive Backbone, Four Causal Discovery Tasks in Event Sequencescited by 0