# Collapsed Amortized Variational Inference for Switching Nonlinear Dynamical Systems

arXiv: https://arxiv.org/abs/1910.09588 · HTML: https://mlsanity.com/paper/1910.09588/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2019.

## Built on by (most cited first, 26 of 26)

- [Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Series](https://mlsanity.com/paper/2301.11308/) (2023)
- [Learning Options via Compression](https://mlsanity.com/paper/2212.04590/) (2022)
- [Deep Explicit Duration Switching Models for Time Series](https://mlsanity.com/paper/2110.13878/) (2021)
- [Graph Switching Dynamical Systems](https://mlsanity.com/paper/2306.00370/) (2023)
- [Distillation of RL Policies with Formal Guarantees via Variational Abstraction of Markov Decision Processes (Technical Report)](https://mlsanity.com/paper/2112.09655/) (2021)
- [Reinforcement Learning in Presence of Discrete Markovian Context Evolution](https://mlsanity.com/paper/2202.06557/) (2022)
- [On the Identifiability of Switching Dynamical Systems](https://mlsanity.com/paper/2305.15925/) (2023)
- [Self-supervised contrastive learning performs non-linear system identification](https://mlsanity.com/paper/2410.14673/) (2024)
- [Hidden Parameter Recurrent State Space Models For Changing Dynamics Scenarios](https://mlsanity.com/paper/2206.14697/) (2022)
- [Continuous Locomotive Crowd Behavior Generation](https://mlsanity.com/paper/2504.04756/) (2025)
- [Conformal Prediction for Time-series Forecasting with Change Points](https://mlsanity.com/paper/2509.02844/) (2025)
- [TRACE: Trajectory Recovery for Continuous Mechanism Evolution in Causal Representation Learning](https://mlsanity.com/paper/2601.21135/) (2026)
- [Segmenting Hybrid Trajectories using Latent ODEs](https://mlsanity.com/paper/2105.03835/) (2021)
- [T-SaS: Toward Shift-aware Dynamic Adaptation for Streaming Data](https://mlsanity.com/paper/2309.02610/) (2023)
- [Maximum Likelihood Learning of Latent Dynamics Without Reconstruction](https://mlsanity.com/paper/2505.23569/) (2025)
- [Amortized Equation Discovery in Hybrid Dynamical Systems](https://mlsanity.com/paper/2406.03818/) (2024)
- [Discovering group dynamics in coordinated time series via hierarchical recurrent switching-state models](https://mlsanity.com/paper/2401.14973/) (2024)
- [A study of animal action segmentation algorithms across supervised, unsupervised, and semi-supervised learning paradigms](https://mlsanity.com/paper/2407.16727/) (2024)
- [End-to-End Identifiable and Consistent Recurrent Switching Dynamical Systems](https://mlsanity.com/paper/2605.06315/) (2026)
- [Switching Recurrent Kalman Networks](https://mlsanity.com/paper/2111.08291/) (2021)
- [Wasserstein Auto-encoded MDPs: Formal Verification of Efficiently Distilled RL Policies with Many-sided Guarantees](https://mlsanity.com/paper/2303.12558/) (2023)
- [Long Range Switching Time Series Prediction via State Space Model](https://mlsanity.com/paper/2407.19201/) (2024)
- [The Recurrent Sticky Hierarchical Dirichlet Process Hidden Markov Model](https://mlsanity.com/paper/2411.04278/) (2024)
- [Bayesian Inference in Recurrent Explicit Duration Switching Linear Dynamical Systems](https://mlsanity.com/paper/2411.04280/) (2024)
- [Deep ZakaiJ: Structured Filtering for Jump-Diffusion Time Series Forecasting](https://mlsanity.com/paper/2605.24548/) (2026)
- [A note on goal-based hierarchical RL](https://mlsanity.com/paper/2609.14605/) (2026)

## Abstract (arXiv)

We propose an efficient inference method for switching nonlinear dynamical systems. The key idea is to learn an inference network which can be used as a proposal distribution for the continuous latent variables, while performing exact marginalization of the discrete latent variables. This allows us to use the reparameterization trick, and apply end-to-end training with stochastic gradient descent. We show that the proposed method can successfully segment time series data, including videos and 3D human pose, into meaningful ``regimes'' by using the piece-wise nonlinear dynamics.