# Sparse Bayesian Estimation of Parameters in Linear-Gaussian State-Space Models

arXiv: https://arxiv.org/abs/2306.11652 · HTML: https://mlsanity.com/paper/2306.11652/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2023.

## Built on by (most cited first, 4 of 4)

- [GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering](https://mlsanity.com/paper/2311.16602/) (2023)
- [BINDy -- Bayesian identification of nonlinear dynamics with reversible-jump Markov-chain Monte-Carlo](https://mlsanity.com/paper/2408.08062/) (2024)
- [Sparse Graphical Linear Dynamical Systems](https://mlsanity.com/paper/2307.03210/) (2023)
- [Deep State-Space Model for Predicting Cryptocurrency Price](https://mlsanity.com/paper/2311.14731/) (2023)

## Abstract (arXiv)

State-space models (SSMs) are a powerful statistical tool for modelling time-varying systems via a latent state. In these models, the latent state is never directly observed. Instead, a sequence of data points related to the state are obtained. The linear-Gaussian state-space model is widely used, since it allows for exact inference when all model parameters are known, however this is rarely the case. The estimation of these parameters is a very challenging but essential task to perform inference and prediction. In the linear-Gaussian model, the state dynamics are described via a state transition matrix. This model parameter is known to behard to estimate, since it encodes the relationships between the state elements, which are never observed. In many applications, this transition matrix is sparse since not all state components directly affect all other state components. However, most parameter estimation methods do not exploit this feature. In this work we propose SpaRJ, a fully probabilistic Bayesian approach that obtains sparse samples from the posterior distribution of the transition matrix. Our method explores sparsity by traversing a set of models that exhibit differing sparsity patterns in the transition matrix. Moreover, we also design new effective rules to explore transition matrices within the same level of sparsity. This novel methodology has strong theoretical guarantees, and unveils the latent structure of the data generating process, thereby enhancing interpretability. The performance of SpaRJ is showcased in example with dimension 144 in the parameter space, and in a numerical example with real data.