Approximate Inference for Multiplicative Latent Force Models
This work addresses a specific inference problem in dynamic systems modeling, but it is incremental as it builds on existing latent force models.
The paper tackled the challenge of performing inference in multiplicative latent force models, which combine mechanistic models with Gaussian process perturbations but lose tractability due to multiplicative interactions, by proposing two approximate inference methods and testing them on simulated and motion capture data.
Latent force models are a class of hybrid models for dynamic systems, combining simple mechanistic models with flexible Gaussian process (GP) perturbations. An extension of this framework to include multiplicative interactions between the state and GP terms allows strong a priori control of the model geometry at the expense of tractable inference. In this paper we consider two methods of carrying out inference within this broader class of models. The first is based on an adaptive gradient matching approximation, and the second is constructed around mixtures of local approximations to the solution. We compare the performance of both methods on simulated data, and also demonstrate an application of the multiplicative latent force model on motion capture data.