- Bayesian nonparametric for modeling time series
- 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.”

- Develop efficient MCMC method based on indian buffet process
- “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.”
- Examples are HMM, switching vector autoregressive process, linear dynamical systems

- “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.” - Behaviors an object can exhibit is described in a feature list, N objects with K features can be described by a NxK matrix
- Beta process is used to infer # of features, Indian buffet process

- “Given a feature set sampled from the IBP, our model reduces to a collection of Bayesian HMMs (or SLDS) with partially shared parameters.”
- Also mention:
- 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.”
- Infinite factorial HMM: “models a single time-series with emissions dependent on a potentially infinite dimensional feature that evolves with independent Markov dynamics.”

- MCMC method is “efficient and exact”
- <This is a little heavy for my faculties at the moment so skimming>
- 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…”
- Mocap experiments
- 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 - Looked at 6 CMU exercise routines. Original data was 62D, they manually selected 12 dimensions from that set, subsample in time as well
- Does a pretty nice job clustering motions

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