Multiplicative Latent Force Models
Bayesian modelling of dynamic systems must achieve a compromise between providing a complete mechanistic specification of the process while retaining the flexibility to handle those situations in which data is sparse relative to model complexity, or a full specification is hard to motivate. Latent force models achieve this dual aim by specifying a parsimonious linear evolution equation with an additive latent Gaussian process (GP) forcing term. In this work we extend the latent force framework to allow for multiplicative interactions between the GP and the latent states leading to more control over the geometry of the trajectories. Unfortunately inference is no longer straightforward and so we introduce an approximation based on the method of successive approximations and examine its performance using a simulation study.
KeywordsGaussian processes Latent force models
The authors would like to thank Dr. Durante and two anonymous referees for their valuable comments and suggestions on an earlier version of this paper, which substantially improved the content and clarity of the article. Daniel J. Tait is supported by an EPSRC studentship.
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