Density propagation for continuous temporal chains. Generative and discriminative models

We analyze non-linear, non-Gaussian temporal chain models (dynamical systems) having continuous hidden states and non-linear, non-Gaussian dynamics and observation models. In this setting we study both discriminative and generative models, describe their underlying independence assumptions, and give the propagation rules for filtering and smoothing. Despite different graphical model structure and independences, the motivation is similar for using either of these models: infer a dynamically varying hidden state, based on sequences of observations. The setting is common in the solution of many inverse problems in artificial intelligence (e.g. computer vision, speech) or control theory. See our companion papers for demonstrations of discriminative [10] and generative [9] models in 3D human motion reconstruction from monocular video applications