Effective Split-Merge Monte Carlo Methods for Nonparametric Models of Sequential Data

Applications of Bayesian nonparametric methods require learning and inference algorithms which efficiently explore models of unbounded complexity. We develop new Markov chain Monte Carlo methods for the beta process hidden Markov model (BP-HMM), enabling discovery of shared activity patterns in large video and motion capture databases. By introducing split-merge moves based on sequential allocation, we allow large global changes in the shared feature structure. We also develop data-driven reversible jump moves which more reliably discover rare or unique behaviors. Our proposals apply to any choice of conjugate likelihood for observed data, and we show success with multinomial, Gaussian, and autoregressive emission models. Together, these innovations allow tractable analysis of hundreds of time series, where previous inference required clever initialization and lengthy burn-in periods for just six sequences.

[1]  Zoubin Ghahramani,et al.  Modeling Dyadic Data with Binary Latent Factors , 2006, NIPS.

[2]  Radford M. Neal,et al.  A Split-Merge Markov chain Monte Carlo Procedure for the Dirichlet Process Mixture Model , 2004 .

[3]  Michael I. Jordan,et al.  Sharing Features among Dynamical Systems with Beta Processes , 2009, NIPS.

[4]  Tu,et al.  Image segmentation by data driven Markov chain Monte Carlo , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[5]  Thomas L. Griffiths,et al.  Nonparametric Latent Feature Models for Link Prediction , 2009, NIPS.

[6]  Erik B. Sudderth,et al.  Nonparametric discovery of activity patterns from video collections , 2012, 2012 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops.

[7]  Michael I. Jordan,et al.  Hierarchical Beta Processes and the Indian Buffet Process , 2007, AISTATS.

[8]  Lars Kai Hansen,et al.  Infinite multiple membership relational modeling for complex networks , 2011, 2011 IEEE International Workshop on Machine Learning for Signal Processing.

[9]  Thomas L. Griffiths,et al.  Infinite latent feature models and the Indian buffet process , 2005, NIPS.

[10]  Carl E. Rasmussen,et al.  Factorial Hidden Markov Models , 1997 .

[11]  Harry Shum,et al.  Image segmentation by data driven Markov chain Monte Carlo , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[12]  Yee Whye Teh,et al.  Beam sampling for the infinite hidden Markov model , 2008, ICML '08.

[13]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[14]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[15]  Jessica K. Hodgins,et al.  Guide to the Carnegie Mellon University Multimodal Activity (CMU-MMAC) Database , 2008 .

[16]  Cordelia Schmid,et al.  Evaluation of Local Spatio-temporal Features for Action Recognition , 2009, BMVC.

[17]  David B. Dahl,et al.  Sequentially-Allocated Merge-Split Sampler for Conjugate and Nonconjugate Dirichlet Process Mixture Models , 2005 .

[18]  Michael I. Jordan,et al.  A Sticky HDP-HMM With Application to Speaker Diarization , 2009, 0905.2592.

[19]  S. L. Scott.  Bayesian Methods for Hidden Markov Models , 2002 .

[20]  Michael I. Jordan,et al.  Hierarchical Dirichlet Processes , 2006 .

[21]  M. Escobar,et al.  Bayesian Density Estimation and Inference Using Mixtures , 1995 .

[22]  Chong Wang,et al.  A Split-Merge MCMC Algorithm for the Hierarchical Dirichlet Process , 2012, ArXiv.

[23]  C. Yau,et al.  Bayesian non‐parametric hidden Markov models with applications in genomics , 2011 .

[24]  Radford M. Neal,et al.  Splitting and merging components of a nonconjugate Dirichlet process mixture model , 2007 .

[25]  Cordelia Schmid,et al.  Learning realistic human actions from movies , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.