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UID:1520@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20170116T153000
DTEND;TZID=Europe/Paris:20170116T163000
DTSTAMP:20170101T143000Z
URL:https://www.i2m.univ-amu.fr/evenements/optimal-scaling-and-convergence
 -of-markov-chain-monte-carlo-methods/
SUMMARY: (...): Optimal scaling and convergence of Markov chain Monte Carlo
  methods
DESCRIPTION:: Sampling over high-dimensional space has become a prerequisit
 e in the applications of Bayesian statistics to machine learning problem. 
 The most common methods for dealing with this problem are Markov Chain Mon
 te Carlo methods.  In this talk\, I will present new insights on the compu
 tational complexity of these algorithms.  First\, I will discuss the optim
 al scaling problem for high-dimensional random walk Metropolis algorithms 
 for densities which are differentiable in Lp mean but which may be irregul
 ar at some points (like the Laplace density for example) and / or are supp
 orted on an interval. The scaling limit is established under assumptions w
 hich are much weaker than the one used in the original derivation of (Robe
 rts\, Gelman\, Gilks\, 1997).  This result has important practical implica
 tions for the use of random walk Metropolisalgorithms in Bayesian framewor
 ks based on sparsity inducing priors.In the second of the talk\, we will p
 resent a method based on the Euler discretization of the Langevin diffusio
 n with either constant or decreasing stepsizes. We will give several new r
 esults allowing convergence to stationarity under different conditions for
  the log-density. A particular attention of these bounds with respect to t
 he dimension of the state space will be paid.http://perso.telecom-paristec
 h.fr/~durmus/
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DTSTART:20161030T020000
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