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SUMMARY:Hierarchical Dirichlet Process Models for Time Series Data - Matth
 ew Beal\, SUNY at Buffalo
DTSTART:20050609T140000Z
DTEND:20050609T150000Z
UID:TALK4377@talks.cam.ac.uk
CONTACT:Phil Cowans
DESCRIPTION:We consider time series data modelling using Hidden Markov Mod
 els  \nhaving an a priori unknown number of hidden states.  We show that t
 he  \nInfinite Hidden Markov Model of Beal\, Ghahramani & Rasmussen (2002)
   \ncan be recast in the framework of Hierarchical Dirichlet Processes  \n
 (HDPs).  The HDP framework (Teh\, Jordan\, Beal & Blei\, 2004) considers  
 \nproblems involving related groups of data: each (fixed) group of data  \
 nis modelled by a DP mixture model\, with the common base measure of  \nth
 e DPs being itself distributed according to a global DP. The base  \nmeasu
 re being discrete w.p.1 ensures that the group DPs share atoms  \n(despite
  being countably infinite).  Teh et al. (2004) present two  \nsampling sch
 emes for posterior inference in the HDP: the Chinese  \nRestaurant Franchi
 se and an auxiliary variable scheme.\n\nWe cast sequential data in the gro
 uped data framework by assigning  \nobservations to groups\, where the gro
 ups are indexed by the value of  \nthe previous state variable in the sequ
 ence\; then the current state  \nand its emission distributions define a g
 roup-specific mixture model.  \nThus the hidden state sequence implicitly 
 defines a partition into  \ngroups\, and induces constraints in the poster
 ior that make the CRF  \nsampling methods proposed quite difficult.  We co
 nstruct an auxiliary  \nvariable sampling scheme for the iHMM\, present re
 sults on some small  \ndata sets and consider an interesting extension for
  language modelling.\n\nJoint work with Yee Whye Teh\, Michael I. Jordan a
 nd David Blei
LOCATION:Small Lecture Theatre\, Cavendish Laboratory
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