Sharing Features among Dynamical Systems with Beta Processes. Fox, Sudderth, Jordan, Willsky. NIPS 2009

  1. Bayesian nonparametric for modeling time series
    1. Beta process prior “approach is based on the discovery of a set of latent dynamical behaviors that are shared among multiple time series.  The size of the set and the sharing pattern are both inferred from data.”
  2. Develop efficient MCMC method based on indian buffet process
  3. “We specifically focus on time series where behaviors can be individually modeled via temporally independent or linear dynamical systems, and where transitions between behaviors are approximately Markovian.”
    1. Examples are HMM, switching vector autoregressive process, linear dynamical systems
  4. “Our approach envisions a large library of behaviors, and each time series or object exhibits a subset of these behaviors.  We then seek a framework for discovering the set of dynamic behaviors that each object exhibits.”
  5. Behaviors an object can exhibit is described in a feature list, N objects with K features can be described by a NxK matrix
    1. Beta process is used to infer # of features, Indian buffet process
  6. “Given a feature set sampled from the IBP, our model reduces to a collection of Bayesian HMMs (or SLDS) with partially shared parameters.”
  7. Also mention:
    1. HDP-HMM: “does not select a subset of behaviors for a given time series, but assumes that all time series share the same set of behaviors and switch among them in exactly the same manner.”
    2. Infinite factorial HMM: “models a single time-series with emissions dependent on a potentially infinite dimensional feature that evolves with independent Markov dynamics.”
  8. MCMC method is “efficient and exact”
  9. <This is a little heavy for my faculties at the moment so skimming>
  10. MCMC interleaves Metropolis-Hastings with Gibbs “We leverage the fact that fixed feature assignments instantiate a set of finite AR-HMMs, for which dynamic programming can be used to efficiently compute marginal likelihoods. Our novel approach to resampling the potentially infinite set of object-specific features employs incremental “birth” and “death” proposals…”
  11. Screen Shot 2014-11-03 at 2.03.04 PM
  12. Mocap experiments
  13. Discusses other methods that have been good for “describing simple human motion…”, “However, there has been little effort in jointly segmenting and identifying common dynamic behaviors amongst a set of multiple motion capture (MoCap) recordings of people performing various tasks.”  BP-AR-HMM does this
  14. Looked at 6 CMU exercise routines.  Original data was 62D, they manually selected 12 dimensions from that set, subsample in time as well
  15. Does a pretty nice job clustering motions

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