Bayesian Nonparametric Learning of Complex Dynamical Phenomena
Through the use of the hierarchical Dirichlet process (HDP), one can examine an HMM with an unbounded number of possible states. We revisit this HDP-HMM and develop a generalization of the model--the sticky HDP-HMM--that allows more robust learning of smoothly varying state dynamics. We demonstrate the utility of the sticky HDP-HMM on the NIST speaker diarization database, segmenting audio files into speaker labels while simultaneously identifying the number of speakers present.
Although the HDP-HMM and its sticky extension are very flexible time series models, they make a strong Markovian assumption that observations are conditionally independent given the discrete HMM state. To better capture the temporal dependencies of real data, we develop extensions of the sticky HDP-HMM for learning SLDS, with applications ranging from the stochastic volatility of financial time series to the dance of honey bees, two examples we use to show the power and flexibility of our Bayesian nonparametric approach.
Finally, in many applications, one would like to discover and model dynamical behaviors which are shared among several related time series. In the latter part of this talk, we consider employing a beta process prior to jointly infer such relationships, and present results on unsupervised segmentation of data from the CMU motion capture database.
Emily B. Fox received the S.B. degree in 2004, M.Eng. degree in 2005, and E.E. degree in 2008 from the Department of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology (MIT). She recently completely her Ph.D. at MIT advised by Prof. Alan Willsky in the Stochastic Systems Group, and is currently a postdoctoral scholar in the Department of Statistical Science at Duke University working with Profs. Mike West and David Dunson.
Emily is a recipient of both the National Defense Science and Engineering Graduate (NDSEG) and National Science Foundation (NSF) fellowships, and currently holds an NSF Mathematical Sciences Postdoctoral Research Fellowship. Her research interests are in multivariate time series analysis and Bayesian nonparametric methods.