High Dimensional Probabilistic Modelling Through Manifolds

Density modelling in high dimensions is a traditionally very difficult problem. Traditional approaches, such as mixtures of Gaussians, typically fail to capture the structure of data sets in high dimensional spaces. In this talk we will argue that for many data sets of interest, the data can be represented as a lower dimensional manifold immersed in the higher dimensional space.  We will then present the Gaussian Process Latent Variable Model (GP-LVM), a non-linear probabilistic variant of principal component analysis (PCA) which implicitly assumes that the data lies on a lower dimensional space.  We will demonstrate the application of the model to a range of data sets, but with a particular focus on human motion data.  We will show some preliminary work on facial animation and make use of a skeletal motion capture data set to illustrate differences between our model and traditional manifold techniques.