BlackBox Inference for NonLinear Latent Force Models
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Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:30883098, 2020.
Abstract
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 nonlinear, 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 blackbox variational inference to jointly estimate the posterior, designing a multivariate extension to local inverse autoregressive flows as a flexible approximator of the system. We compare estimates on systems where the posterior is known, demonstrating the effectiveness of the approximation, and apply to problems with nonlinear dynamics, multioutput systems and models with nonGaussian likelihoods.
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