# Linear Variational State-Space Filtering

arXiv: https://arxiv.org/abs/2201.01353 · HTML: https://mlsanity.com/paper/2201.01353/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 4 Jan 2022.

## Builds on (most cited first, 23 of 23)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [AirSim: High-Fidelity Visual and Physical Simulation for Autonomous Vehicles](https://mlsanity.com/paper/1705.05065/) (2017)
- [Lossy Image Compression with Compressive Autoencoders](https://mlsanity.com/paper/1703.00395/) (2017)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Stochastic Video Generation with a Learned Prior](https://mlsanity.com/paper/1802.07687/) (2018)
- [Stochastic Variational Video Prediction](https://mlsanity.com/paper/1710.11252/) (2017)
- [Stochastic Latent Actor-Critic: Deep Reinforcement Learning with a Latent Variable Model](https://mlsanity.com/paper/1907.00953/) (2019)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [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)
- [Self-Supervised Visual Representation Learning from Hierarchical Grouping](https://mlsanity.com/paper/2012.03044/) (2020)
- [Robust Locally-Linear Controllable Embedding](https://mlsanity.com/paper/1710.05373/) (2017)
- [Video Autoencoder: self-supervised disentanglement of static 3D structure and motion](https://mlsanity.com/paper/2110.02951/) (2021)
- [Online Variational Filtering and Parameter Learning](https://mlsanity.com/paper/2110.13549/) (2021)
- [Mind the Gap when Conditioning Amortised Inference in Sequential Latent-Variable Models](https://mlsanity.com/paper/2101.07046/) (2021)
- [An Auto-Encoder Strategy for Adaptive Image Segmentation](https://mlsanity.com/paper/2004.13903/) (2020)

## Abstract (arXiv)

We introduce Variational State-Space Filters (VSSF), a new method for unsupervised learning, identification, and filtering of latent Markov state space models from raw pixels. We present a theoretically sound framework for latent state space inference under heterogeneous sensor configurations. The resulting model can integrate an arbitrary subset of the sensor measurements used during training, enabling the learning of semi-supervised state representations, thus enforcing that certain components of the learned latent state space to agree with interpretable measurements. From this framework we derive L-VSSF, an explicit instantiation of this model with linear latent dynamics and Gaussian distribution parameterizations. We experimentally demonstrate L-VSSF's ability to filter in latent space beyond the sequence length of the training dataset across several different test environments.