Revisiting Gaussian process dynamical models

The recently proposed Gaussian process dynamical models (GPDMs) have been successfully applied to time series modeling. There are four learning algorithms for GPDMs: maximizing a posterior (MAP), fixing the kernel hyperparameters α¯ (Fix.α¯), balanced GPDM (B-GPDM) and two-stage MAP (T.MAP), which are designed for model training with complete data. When data are incomplete, GPDMs reconstruct the missing data using a function of the latent variables before parameter updates, which, however, may cause cumulative errors. In this paper, we present four new algorithms (MAP⁺, Fix.α¯⁺, B-GPDM⁺ and T.MAP⁺) for learning GPDMs with incomplete training data and a new conditional model (CM⁺) for recovering incomplete test data. Our methods adopt the Bayesian framework and can fully and properly use the partially observed data. We conduct experiments on incomplete motion capture data (walk, run, swing and multiple-walker) and make comparisons with the existing four algorithms as well as k-NN, spline interpolation and VGPDS. Our methods perform much better on both training with incomplete data and recovering incomplete test data.