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SUMMARY:Bayesian nonparametric latent feature models - Zoubin Ghahramani
DTSTART:20070502T130000Z
DTEND:20070502T140000Z
UID:TALK6749@talks.cam.ac.uk
CONTACT:Christian Steinruecken
DESCRIPTION:Latent variables are an important component of many statistica
 l models. Most latent variable models\, such as mixture models\, factor an
 alysis\, and independent components analysis (ICA)\, assume a finite\, usu
 ally small number of latent variables.  However\, it may be statistically 
 undesirable to constrain the number of latent variables a priori. Here we 
 show how a more flexible nonparametric approach is possible in which the n
 umber of latent variables is unbounded. To do\nthis\, we describe a probab
 ility distribution over equivalence classes of binary matrices with a fini
 te number of rows\, corresponding to the data points\, and an unbounded nu
 mber of columns\, corresponding to the\nlatent variables. Each data point 
 can be associated with a subset of the possible latent variables\, which w
 e refer to as the latent features of that data point. The binary variables
  in the matrix indicate which latent feature is possessed by which data po
 int\, and\nthere is a potentially infinite array of features.  We derive t
 he distribution over unbounded binary matrices by taking the limit of a di
 stribution over $N \\times K$ binary matrices as $K \\rightarrow \\infty$\
 , a strategy inspired by the derivation of the Chinese\nrestaurant process
  (Aldous\, 1985\; Pitman\, 2002) which preserves exchangeability of the ro
 ws. We define a simple generative processes for this distribution which we
  call the Indian buffet process (IBP\; Griffiths and Ghahramani\, 2005).  
 We describe recent extensions of this model\, Markov chain Monte Carlo alg
 orithms for inference\,  and a number of applications to collaborative fil
 tering\, independent components analysis\, bioinformatics\, cognitive mode
 lling\, and causal discovery.\n\nJoint work with Thomas L. Griffiths (UC B
 erkeley).  \n\n
LOCATION:TCM Seminar Room\, Cavendish Laboratory\, Department of Physics
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