Dynamic dependence analysis : modeling and inference of changing dependence among multiple time-series

[摘要] (cont.) Second, we develop a Bayesian approach and present a conjugate prior on the parameters and structure of a model describing the dependence among time-series. This allows for Bayesian reasoning over structure while integrating over parameters. The modular nature of the prior we define allows one to reason over a super-exponential number of structures in exponential-time in general. Furthermore, by imposing simple local or global structural constraints we show that one can reduce the exponential-time complexity to polynomial-time complexity while still reasoning over a super-exponential number of candidate structures. We cast the problem of reasoning over temporally evolving structures as inference over a latent state sequence which indexes structure over time in a dynamic Bayesian network. This model allows one to utilize standard algorithms such as Expectation Maximization, Viterbi decoding, forward-backward messaging and Gibbs sampling in order to efficiently reasoning over an exponential number of structural sequences. We demonstrate the utility of our methodology on two tasks: audio-visual association and moving object interaction analysis. We achieve state-of-the-art performance on a standard audio-visual dataset and show how our model allows one to tractably make exact probabilistic statements about interactions among multiple moving objects.

[发布机构] Massachusetts Institute of Technology