# Neural State-Space Modeling with Latent Causal-Effect Disentanglement

arXiv: https://arxiv.org/abs/2209.12387 · HTML: https://mlsanity.com/paper/2209.12387/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 19 references that are in the map.
- First posted on arXiv 26 Sep 2022.

## Builds on (most cited first, 14 of 14)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [ODE2VAE: Deep generative second order ODEs with Bayesian neural networks](https://mlsanity.com/paper/1905.10994/) (2019)
- [Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2102.00397/) (2021)
- [Neural Ordinary Differential Equations for Intervention Modeling](https://mlsanity.com/paper/2010.08304/) (2020)
- [Generative Modeling and Inverse Imaging of Cardiac Transmembrane Potential](https://mlsanity.com/paper/1905.04803/) (2019)
- [Learning Geometry-Dependent and Physics-Based Inverse Image Reconstruction](https://mlsanity.com/paper/2007.09522/) (2020)

## Abstract (arXiv)

Despite substantial progress in deep learning approaches to time-series reconstruction, no existing methods are designed to uncover local activities with minute signal strength due to their negligible contribution to the optimization loss. Such local activities however can signify important abnormal events in physiological systems, such as an extra foci triggering an abnormal propagation of electrical waves in the heart. We discuss a novel technique for reconstructing such local activity that, while small in signal strength, is the cause of subsequent global activities that have larger signal strength. Our central innovation is to approach this by explicitly modeling and disentangling how the latent state of a system is influenced by potential hidden internal interventions. In a novel neural formulation of state-space models (SSMs), we first introduce causal-effect modeling of the latent dynamics via a system of interacting neural ODEs that separately describes 1) the continuous-time dynamics of the internal intervention, and 2) its effect on the trajectory of the system's native state. Because the intervention can not be directly observed but have to be disentangled from the observed subsequent effect, we integrate knowledge of the native intervention-free dynamics of a system, and infer the hidden intervention by assuming it to be responsible for differences observed between the actual and hypothetical intervention-free dynamics. We demonstrated a proof-of-concept of the presented framework on reconstructing ectopic foci disrupting the course of normal cardiac electrical propagation from remote observations.