Indian buffet process for model selection in latent force models

Abstract

Latent force models (LFM) are an hybrid approach which combines multiple output Gaussian processes and differential equations, where the covariance functions encode the physical models given by the differential equations. LFM require the specification of the number of latent functions used to build the covariance function for the outputs. Furthermore, they assume that the output data is explained by using the entire set of latent functions, which is not the case in many real applications. We propose in this paper the use of an Indian Buffet process (IBP) as a way to perform model selection over the number of latent Gaussian processes in LFM applications. Furthermore, IBP allows us to infer the interconnection between latent functions and the outputs. We use variational inference to approximate the posterior distributions, and show examples of the proposed model performance over artificial data and a motion capture dataset.