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SUMMARY:Approximate Bayesian Inference for Large Scale Inverse Problems: A
  Computational Viewpoint - Prof. Matthias Seeger (EPFL)
DTSTART:20110728T103000Z
DTEND:20110728T113000Z
UID:TALK32198@talks.cam.ac.uk
CONTACT:Zoubin Ghahramani
DESCRIPTION:Tomographic sparse linear inverse problems are at the core of 
 medical imaging\n(MRI\, CT)\, astronomy\, analysis of large scale networks
 \, and many other\napplications. Viewed as a probabilistic graphical model
 \, they are characterized\nby a densely\, non-locally coupled likelihood a
 nd a non-Gaussian sparsity\nprior. Even MAP estimation is challenging for 
 these models\, yet intense\nrecent research has produced a range of compet
 itive MAP algorithms. However\,\nfor these underdetermined problems\, ther
 e are compelling reasons to move\nbeyond MAP towards Bayesian inference an
 d decision making\, such as increased\nrobustness and interpretability\, b
 uilt-in mechanisms to fit linear or nonlinear\nhyperparameters\, and adapt
 ation of the measurement operator by experimental\ndesign (active learning
 ). Unfortunately\, current approximate inference\nalgorithms are many orde
 rs of magnitude too slow to accept this challenge.\n\nA key strategy to na
 rrow the gap to MAP is to find ways to reduce approximate\ninference to su
 bproblems of penalized likelihood structure. Using tools from\nconvex dual
 ity\, I show how to achieve such iterative decoupling for a range\nof comm
 only used variational inference relaxations. Resulting double loop\nalgori
 thms are orders of magnitude faster than previous coordinate descent\n(or 
 "message-passing") algorithms. Not surprisingly\, approximate inference\nr
 emains harder than MAP\, but the added difficulties are transparent and\na
 menable to fast techniques from signal processing and numerical mathematic
 s.\n\nTime permitting\, I will comment on work in progress on integrating 
 factorization\nassumptions and on approximate Bayesian blind deconvolution
 .\n
LOCATION:Engineering Department\, CBL Room 438
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