Hierarchical Bayesian Embeddings for Analysis and Synthesis of High-Dimensional Dynamic Data

High-dimensional, time-dependent data are analyzed by developing a dynamic model in an associated low-dimensional embedding space. The proposed approach employs hierarchical Bayesian methods to learn a reversible statistical embedding, allowing one to (i) estimate the latent-space dimension from a set of training data, (ii) discard the training data when embedding new data, and (iii) synthesize high-dimensional data from the embedding space. Properties (i)-(iii) are useful for the general analysis of high-dimensional data, even in the absence of time dependence. For the case of dynamic data, hierarchical Bayesian methods are employed to learn a nonlinear dynamic model in the low-dimensional embedding space, allowing joint analysis of multiple types of dynamic data, sharing strength and inferring inter-relationships in dynamic data. Combined, the overall learned model enables the analysis and synthesis of high-dimensional dynamic data. Example results are presented for statistical embedding, latent-space dimensionality estimation, and analysis and synthesis of high-dimensional (dynamic) motion-capture data.