# Learning Latent Causal Dynamics

arXiv: https://arxiv.org/abs/2202.04828 · HTML: https://mlsanity.com/paper/2202.04828/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 44 references that are in the map.
- First posted on arXiv 10 Feb 2022.

## Builds on (most cited first, 20 of 20)

- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [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)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Coding](https://mlsanity.com/paper/2007.10930/) (2020)
- [Disentangled Sequential Autoencoder](https://mlsanity.com/paper/1803.02991/) (2018)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)](https://mlsanity.com/paper/2001.04872/) (2020)
- [Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series](https://mlsanity.com/paper/2006.12107/) (2020)
- [Causal Discovery in Physical Systems from Videos](https://mlsanity.com/paper/2007.00631/) (2020)
- [Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA](https://mlsanity.com/paper/2106.09620/) (2021)
- [Contrast and Mix: Temporal Contrastive Video Domain Adaptation with Background Mixing](https://mlsanity.com/paper/2110.15128/) (2021)
- [AdaRL: What, Where, and How to Adapt in Transfer Reinforcement Learning](https://mlsanity.com/paper/2107.02729/) (2021)
- [Inference via low-dimensional couplings](https://mlsanity.com/paper/1703.06131/) (2017)

## Built on by (most cited first, 13 of 13)

- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Temporally Disentangled Representation Learning](https://mlsanity.com/paper/2210.13647/) (2022)
- [Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems](https://mlsanity.com/paper/2206.06169/) (2022)
- [Identifying Weight-Variant Latent Causal Models](https://mlsanity.com/paper/2208.14153/) (2022)
- [Causal Representation Learning Made Identifiable by Grouping of Observational Variables](https://mlsanity.com/paper/2310.15709/) (2023)
- [Identification of Nonlinear Latent Hierarchical Models](https://mlsanity.com/paper/2306.07916/) (2023)
- [Identifiable Latent Polynomial Causal Models Through the Lens of Change](https://mlsanity.com/paper/2310.15580/) (2023)
- [Fine-Grained Causal Dynamics Learning with Quantization for Improving Robustness in Reinforcement Learning](https://mlsanity.com/paper/2406.03234/) (2024)
- [Towards Identifiable Latent Additive Noise Models](https://mlsanity.com/paper/2403.15711/) (2024)
- [Curious Causality-Seeking Agents Learn Meta Causal World](https://mlsanity.com/paper/2506.23068/) (2025)
- [Measure-Theoretic Anti-Causal Representation Learning](https://mlsanity.com/paper/2510.18052/) (2025)
- [On the Identifiability of Quantized Factors](https://mlsanity.com/paper/2306.16334/) (2023)
- [MoVA: Learning Asymmetric Dual Projections for Modular Long Video-Text Alignment](https://mlsanity.com/paper/2607.00858/) (2026)

## Abstract (arXiv)

One critical challenge of time-series modeling is how to learn and quickly correct the model under unknown distribution shifts. In this work, we propose a principled framework, called LiLY, to first recover time-delayed latent causal variables and identify their relations from measured temporal data under different distribution shifts. The correction step is then formulated as learning the low-dimensional change factors with a few samples from the new environment, leveraging the identified causal structure. Specifically, the framework factorizes unknown distribution shifts into transition distribution changes caused by fixed dynamics and time-varying latent causal relations, and by global changes in observation. We establish the identifiability theories of nonparametric latent causal dynamics from their nonlinear mixtures under fixed dynamics and under changes. Through experiments, we show that time-delayed latent causal influences are reliably identified from observed variables under different distribution changes. By exploiting this modular representation of changes, we can efficiently learn to correct the model under unknown distribution shifts with only a few samples.