# Semi-Supervised Model-Free Bayesian State Estimation from Compressed Measurements

arXiv: https://arxiv.org/abs/2407.07368 · HTML: https://mlsanity.com/paper/2407.07368/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 50 references that are in the map.
- First posted on arXiv 10 Jul 2024.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
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- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [A Survey on Deep Semi-supervised Learning](https://mlsanity.com/paper/2103.00550/) (2021)
- [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)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [Combining Generative and Discriminative Models for Hybrid Inference](https://mlsanity.com/paper/1906.02547/) (2019)
- [Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC](https://mlsanity.com/paper/1306.2861/) (2013)
- [DANSE: Data-driven Non-linear State Estimation of Model-free Process in Unsupervised Learning Setup](https://mlsanity.com/paper/2306.03897/) (2023)
- [Computationally Efficient Bayesian Learning of Gaussian Process State Space Models](https://mlsanity.com/paper/1506.02267/) (2015)
- [Unsupervised Learned Kalman Filtering](https://mlsanity.com/paper/2110.09005/) (2021)
- [End-To-End Semi-supervised Learning for Differentiable Particle Filters](https://mlsanity.com/paper/2011.05748/) (2020)
- [Adaptive KalmanNet: Data-Driven Kalman Filter with Fast Adaptation](https://mlsanity.com/paper/2309.07016/) (2023)
- [From Target Tracking to Targeting Track: A Data-Driven Yet Analytical Approach to Joint Target Detection and Tracking](https://mlsanity.com/paper/2104.11122/) (2021)
- [Bayesian Semisupervised Learning with Deep Generative Models](https://mlsanity.com/paper/1706.09751/) (2017)

## Built on by (most cited first, 1 of 1)

- [pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements](https://mlsanity.com/paper/2510.27503/) (2025)

## Abstract (arXiv)

We consider data-driven Bayesian state estimation from compressed measurements (BSCM) of a model-free process. The dimension of the temporal measurement vector is lower than that of the temporal state vector to be estimated, leading to an under-determined inverse problem. The underlying dynamical model of the state's evolution is unknown for a `model-free process.' Hence, it is difficult to use traditional model-driven methods, for example, Kalman and particle filters. Instead, we consider data-driven methods. We experimentally show that two existing unsupervised learning-based data-driven methods fail to address the BSCM problem in a model-free process. The methods are -- data-driven nonlinear state estimation (DANSE) and deep Markov model (DMM). While DANSE provides good predictive/forecasting performance to model the temporal measurement data as a time series, its unsupervised learning lacks suitable regularization for tackling the BSCM task. We then propose a semi-supervised learning approach and develop a semi-supervised learning-based DANSE method, referred to as SemiDANSE. In SemiDANSE, we use a large amount of unlabelled data along with a limited amount of labelled data, i.e., pairwise measurement-and-state data, which provides the desired regularization. Using {benchmark chaotic dynamical systems}, we {empirically} show that the data-driven SemiDANSE provides competitive state estimation performance for BSCM {using a handful of different measurement systems}, against a hybrid method called KalmanNet and two model-driven methods (extended Kalman filter and unscented Kalman filter) that know the dynamical models exactly.