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

arXiv: https://arxiv.org/abs/2210.14706 · HTML: https://mlsanity.com/paper/2210.14706/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 53 references that are in the map.
- First posted on arXiv 26 Oct 2022.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [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)
- [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)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [Conditional Density Estimation with Bayesian Normalising Flows](https://mlsanity.com/paper/1802.04908/) (2018)
- [Causal Inference for Time series Analysis: Problems, Methods and Evaluation](https://mlsanity.com/paper/2102.05829/) (2021)
- [Invertible Generative Modeling using Linear Rational Splines](https://mlsanity.com/paper/2001.05168/) (2020)
- [Neural Additive Vector Autoregression Models for Causal Discovery in Time Series](https://mlsanity.com/paper/2010.09429/) (2020)
- [Neural Granger Causality](https://mlsanity.com/paper/1802.05842/) (2018)
- [Discovering Nonlinear Relations with Minimum Predictive Information Regularization](https://mlsanity.com/paper/2001.01885/) (2020)
- [Variable-lag Granger Causality for Time Series Analysis](https://mlsanity.com/paper/1912.10829/) (2019)
- [Granger Causality in Multi-variate Time Series using a Time Ordered Restricted Vector Autoregressive Model](https://mlsanity.com/paper/1511.03463/) (2015)
- [seq2graph: Discovering Dynamic Dependencies from Multivariate Time Series with Multi-level Attention](https://mlsanity.com/paper/1812.04448/) (2018)

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

- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Mitigating Modality Prior-Induced Hallucinations in Multimodal Large Language Models via Deciphering Attention Causality](https://mlsanity.com/paper/2410.04780/) (2024)
- [CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discovery](https://mlsanity.com/paper/2310.01753/) (2023)
- [BayesDAG: Gradient-Based Posterior Inference for Causal Discovery](https://mlsanity.com/paper/2307.13917/) (2023)
- [Neural Structure Learning with Stochastic Differential Equations](https://mlsanity.com/paper/2311.03309/) (2023)
- [Deep Causal Learning: Representation, Discovery and Inference](https://mlsanity.com/paper/2211.03374/) (2022)
- [Discovering Mixtures of Structural Causal Models from Time Series Data](https://mlsanity.com/paper/2310.06312/) (2023)
- [On the Identifiability of Switching Dynamical Systems](https://mlsanity.com/paper/2305.15925/) (2023)
- [Jacobian Regularizer-based Neural Granger Causality](https://mlsanity.com/paper/2405.08779/) (2024)
- [Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis](https://mlsanity.com/paper/2501.12500/) (2025)
- [Double Machine Learning Based Structure Identification from Temporal Data](https://mlsanity.com/paper/2311.06012/) (2023)
- [ClimateBench-M: A Multi-Modal Climate Data Benchmark with a Simple Generative Method](https://mlsanity.com/paper/2504.07394/) (2025)
- [Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises](https://mlsanity.com/paper/2506.17065/) (2025)
- [Causal Temporal Regime Structure Learning](https://mlsanity.com/paper/2311.01412/) (2023)
- [LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Data](https://mlsanity.com/paper/2410.19464/) (2024)
- [CausalStock: Deep End-to-end Causal Discovery for News-driven Stock Movement Prediction](https://mlsanity.com/paper/2411.06391/) (2024)
- [Causal Discovery for Irregularly Time Series with Consistency Guarantees](https://mlsanity.com/paper/2507.03310/) (2025)
- [Identifying Unique Spatial-Temporal Bayesian Network without Markov Equivalence](https://mlsanity.com/paper/2211.10085/) (2022)
- [Bayesian Vector AutoRegression with Factorised Granger-Causal Graphs](https://mlsanity.com/paper/2402.03614/) (2024)
- [Identifying Nonstationary Causal Structures with High-Order Markov Switching Models](https://mlsanity.com/paper/2406.17698/) (2024)
- [Discovering Latent Causal Graphs from Spatiotemporal Data](https://mlsanity.com/paper/2411.05331/) (2024)
- [Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families](https://mlsanity.com/paper/2606.02231/) (2026)
- [The Failures of Marginal Influence-Based Attribution Methods for Global Time Series Explanations](https://mlsanity.com/paper/2607.16236/) (2026)
- [SpinSVAR: Estimating Structural Vector Autoregression Assuming Sparse Input](https://mlsanity.com/paper/2501.03130/) (2025)
- [Robust Causal Discovery in Real-World Time Series with Power-Laws](https://mlsanity.com/paper/2507.12257/) (2025)
- [PRCD-MAP: Learning How Much to Trust Imperfect Priors in Causal Discovery](https://mlsanity.com/paper/2605.01669/) (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)
- [ITSY: Causal Discovery From Irregular Time-Series Data](https://mlsanity.com/paper/2609.23516/) (2026)
- [seq2cause: One Autoregressive Backbone, Four Causal Discovery Tasks in Event Sequences](https://mlsanity.com/paper/2609.31801/) (2026)

## 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.