Variational State and Parameter Estimation

TL;DR

This paper introduces a variational method for efficiently estimating both states and parameters in nonlinear state-space models, offering a deterministic alternative to traditional sampling techniques.

Contribution

It proposes a novel variational approach that approximates intractable Bayesian distributions with an assumed density, enabling efficient joint state and parameter estimation.

Findings

Outperforms Hamiltonian Monte Carlo in numerical examples

Provides a deterministic and efficient estimation framework

Facilitates derivatives for optimization due to density parametrization

Abstract

This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this work, a variational approach is used to provide an assumed density which approximates the desired, intractable, distribution. The approach is deterministic and results in an optimisation problem of a standard form. Due to the parametrisation of the assumed density selected first- and second-order derivatives are readily available which allows for efficient solutions. The proposed method is compared against state-of-the-art Hamiltonian Monte Carlo in two numerical examples.