We consider linear dynamical systems, particularly coupled linear oscillators, where the parameters represent meaningful values in a domain theory and thus learning what affects them contributes to explanation. Rather than allow perturbations of latent states, we assume that temporal variation beyond noise is explained by parameter drift, and variation across coupled systems is a function of moderating variables. This change of focus reduces opportunities for efficient inference, and we propose sampling procedures to learn and fit the models. We test our approach on a real dataset of physiological measures of heterosexual couples engaged in a conversation about a potentially emotional topic, with body mass index (BMI) being considered as a moderator. We evaluate several models on their ability to predict future conversation dynamics (the last 20% of the data for each test couple), with shared parameters being learned using held out data. As proof of concept, we validate the hypothesis that BMI affects the conversation dynamic in the experimentally chosen topic.

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.