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SUMMARY:Consistency and CLTs for stochastic gradient Langevin dynamics bas
 ed on subsampled data - Vollmer\, S (University of Oxford)
DTSTART:20140424T145000Z
DTEND:20140424T152500Z
UID:TALK52165@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: Alexandre Thiery (National University of Singapore
 )\, Yee-Whye Teh (University of Oxford) \n\nApplying MCMC to large data se
 ts is expensive. Both calculating the acceptance probability and creating 
 informed proposals depending on the likelihood require an iteration throug
 h the whole data set. The recently proposed Stochastic Gradient Langevin D
 ynamics (SGLD) circumvents this problem by generating proposals based on o
 nly a subset of the data and skipping the accept-reject step. In order to 
 heuristically justify the latter\, the step size converges to zero in a no
 n-summable way. \n\nUnder appropriate Lyapunov conditions\, we provide a r
 igorous foundation for this algorithm by showing consistency of the weight
 ed sample average and proving a CLT for it. Surprisingly\, the fraction of
  the data subset selection does not have an influence on the asymptotic va
 riance.\n
LOCATION:Seminar Room 1\, Newton Institute
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