The combinatorial structure underlying a beta processes is that of a continuum of Blackwell-MacQueen urn schemes

Add to your list(s) Download to your calendar using vCal

• Dr Daniel Roy (University of Cambridge)
• Tuesday 20 November 2012, 13:00-14:30
• Engineering Department, CBL Room BE-438.

If you have a question about this talk, please contact Konstantina Palla.

We uncover a novel urn scheme underlying conditionally independent sequences of Bernoulli processes that share a common beta process hazard measure. As shown by Thibaux and Jordan (2007), in the special case when the underlying beta process has a constant concentration function and a finite and non-atomic base measure, the combinatorial structure is that of the Indian buffet process (IBP) introduced by Griffiths and Ghahramani (2005). By reinterpreting the beta process introduced by Hjort (1990) as a continuum of Dirichlet processes, we obtain a simple predictive rule for the general case, and then show that a continuum of Pitman-Yor processes recovers a three-parameter variant of the IBP introduced by Teh and Gorur (2009) that exhibits power-law behavior, as further studied by Broderick, Pitman and Jordan (2012). The idea extends to arbitrary exchangeable partition probability functions. In the same way that hierarchies of Dirichlet processes can be given Chinese restaurant franchise representations as shown by Teh, Jordan, Beal and Blei (2006), one can construct representations of hierarchies of beta processes using the stochastic process we uncover. This new perspective has obvious implications for inference algorithms.

This talk is part of the Machine Learning @ CUED series.

This talk is included in these lists:

• Seminar
• All Talks (aka the CURE list)
• Biology
• CBL important
• Cambridge Centre for Data-Driven Discovery (C2D3)
• Cambridge Forum of Science and Humanities
• Cambridge Language Sciences
• Cambridge Neuroscience Seminars
• Cambridge talks
• Chris Davis' list
• Creating transparent intact animal organs for high-resolution 3D deep-tissue imaging
• Engineering Department, CBL Room BE-438
• Featured lists
• Guy Emerson's list
• Hanchen DaDaDash
• Inference Group Summary
• Information Engineering Division seminar list
• Interested Talks
• Joint Machine Learning Seminars
• Life Science
• Life Sciences
• ML
• Machine Learning @ CUED
• Machine Learning Summary
• Neuroscience
• Neuroscience Seminars
• Neuroscience Seminars
• Required lists for MLG
• Simon Baker's List
• Stem Cells & Regenerative Medicine
• Trust & Technology Initiative - interesting events
• bld31
• dh539
• kt532's list
• ndk22's list
• ob366-ai4er
• rp587
• yk373's list

Note that ex-directory lists are not shown.