Sparse Bayesian Estimation of Parameters in Linear-Gaussian State-Space Models
arXiv:2306.11652 · doi:10.1109/TSP.2023.3278867
Abstract
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.
arXiv comment15 pages double column
References in corpus (11)
- Variational Inference: A Review for Statisticians
- A fast approach for overcomplete sparse decomposition based on smoothed L0 norm
- On Particle Methods for Parameter Estimation in State-Space Models
- How to generate random matrices from the classical compact groups
- Cooperative Parallel Particle Filters for online model selection and applications to Urban Mobility
- Marginal likelihood computation for model selection and hypothesis testing: an extensive review
- DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks
- On the safe use of prior densities for Bayesian model selection
- Graphical Inference in Linear-Gaussian State-Space Models
- DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization
- Weak Convergence and Optimal Tuning of the Reversible Jump Algorithm