Bayesian Switching Interaction Analysis Under Uncertainty

We introduce a Bayesian discrete-time framework for switching-interaction analysis under uncertainty, in which latent interactions, switching pattern and signal states and dynamics are inferred from noisy (and possibly missing) observations of these signals. We propose reasoning over full posterior distribution of these latent variables as a means of combating and characterizing uncertainty. This approach also allows for answering a variety of questions probabilistically, which is suitable for exploratory pattern discovery and post-analysis by human experts. This framework is based on a fully-Bayesian learning of the structure of a switching dynamic Bayesian network (DBN) and utilizes a state-space approach to allow for noisy observations and missing data. It generalizes the autoregressive switching interaction model of Siracusa et al., which does not allow observation noise, and the switching linear dynamic system model of Fox et al., which does not infer interactions among signals. Posterior samples are obtained via a Gibbs sampling procedure, which is particularly efficient in the case of linear Gaussian dynamics and observation models. We demonstrate the utility of our framework on a controlled human-generated data, and a real-world climate data.