We describe a generalization of the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) which is able to encode prior information that state transitions are more likely between “nearby” states. This is accomplished by defining a similarity function on the state space and scaling transition probabilities by pairwise similarities, thereby inducing correlations among the transition distributions. We present an augmented data representation of the model as a Markov Jump Process in which: (1) some jump attempts fail, and (2) the probability of success is proportional to the similarity between the source and destination states. This augmentation restores conditional conjugacy and admits a simple Gibbs sampler. We evaluate the model and inference method on a speaker diarization task and a “harmonic parsing” task using four-part chorale data, as well as on several synthetic datasets, achieving favorable comparisons to existing models.

We develop a Bayesian modeling approach for tracking people in 3D from monocular video with unknown cameras. Modeling in 3D provides natural explanations for occlusions and smoothness discontinuities that result from projection, and allows priors on velocity and smoothness to be grounded in physical quantities: meters and seconds vs. pixels and frames. We pose the problem in the context of data association, in which observations are assigned to tracks. A correct application of Bayesian inference to multi-target tracking must address the fact that the model's dimension changes as tracks are added or removed, and thus, posterior densities of different hypotheses are not comparable. We address this by marginalizing out the trajectory parameters so the resulting posterior over data associations has constant dimension. This is made tractable by using (a) Gaussian process priors for smooth trajectories and (b) approximately Gaussian likelihood functions. Our approach provides a principled method for incorporating multiple sources of evidence, we present results using both optical flow and object detector outputs. Results are comparable to recent work on 3D tracking and, unlike others, our method requires no pre-calibrated cameras.