Black-Box Inference for Non-Linear Latent Force Models
This work addresses inference difficulties in mechanistic models with unknown forcing terms, though it appears incremental as an extension of existing variational inference techniques.
The paper tackles the challenge of estimating posterior states and forcing terms in non-linear latent force models with unknown system parameters by using black-box variational inference with a multivariate extension to local inverse autoregressive flows. The method demonstrates effectiveness on systems with known posteriors and applies to non-linear dynamics, multi-output systems, and non-Gaussian likelihoods.
Latent force models are systems whereby there is a mechanistic model describing the dynamics of the system state, with some unknown forcing term that is approximated with a Gaussian process. If such dynamics are non-linear, it can be difficult to estimate the posterior state and forcing term jointly, particularly when there are system parameters that also need estimating. This paper uses black-box variational inference to jointly estimate the posterior, designing a multivariate extension to local inverse autoregressive flows as a flexible approximater of the system. We compare estimates on systems where the posterior is known, demonstrating the effectiveness of the approximation, and apply to problems with non-linear dynamics, multi-output systems and models with non-Gaussian likelihoods.