Gaussian Process Dynamical Models. Wang, Fleet, Hertzmann. Nips 2006

“A GPDM comprises a low-dimensional latent space with associated dynamics, and a map from the latent space to an observation space.”

“We demonstrate the approach on human motion capture data in which each pose is 62-dimensional.”

“we show that integrating over parameters in nonlinear dynamical systems can also be performed in closed-form. The resulting Gaussian Process Dynamical Model (GPDM) is fully defined by a set of lowdimensional representations of the training data, with both dynamics and observation mappings learned from GP regression.”

As a Bayesian nonparametric, GPs make them easier to use and overfit less

“Despite the large state space, the space of activity-specific human poses and motions has a much smaller intrinsic dimensionality; in our experiments with walking and golf swings, 3 dimensions often suffice.”

“The Gaussian Process Dynamical Model (GPDM) comprises a mapping from a latent space to the data space, and a dynamical model in the latent space…The GPDM is obtained by marginalizing out the parameters of the two mappings, and optimizing the latent coordinates of training data.”

“t should be noted that, due to the nonlinear dynamical mapping in (3), the joint distribution of the latent coordinates is not Gaussian. Moreover, while the density over the initial state may be Gaussian, it will not remain Gaussian once propagated through the dynamics.”

Looks like all predictions are 1-step, can specifically set it up to use more history to make it higher-order

“In effect, the GPDM models a high probability “tube” around the data.”

“Here we consider a simple online method for generating a new motion, called mean-prediction, which avoids the relatively expensive Monte Carlo sampling used above.”

<Wordpress ate the rest of this post. A very relevant paper I should follow up on.>