Graphical Models for Time-Series

Time-series analysis is central to many problems in signal processing, including acoustics, image processing, vision, tracking, information retrieval, and finance, to name a few. Because of the wide base of application areas, having a common description of the models is useful in transferring ideas between the various communities. Graphical models provide a compact way to represent such models and thereby rapidly transfer ideas. We will discuss briefly how classical timeseries models such as Kalman filters and hidden Markov models (HMMs) can be represented as graphical models and critically how this representation differs from other common graphical representations such as state-transition and block diagrams. We will use this framework to show how one may easily envisage novel models and gain insight into their computational implementation.