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SUMMARY:Concentration of tempered posteriors and of their variational appr
 oximations - Pierre Alquier\, ENSAE
DTSTART:20181116T160000Z
DTEND:20181116T170000Z
UID:TALK109672@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:While Bayesian methods are extremely popular in statistics and
  machine learning\, their application to massive datasets is often challen
 ging\, when possible at all. Indeed\, the classical MCMC algorithms are pr
 ohibitively slow when both the model dimension and the sample size are lar
 ge. Variational Bayesian methods aim at approximating the posterior by a d
 istribution in a tractable family. Thus\, MCMC are replaced by an optimiza
 tion algorithm which is orders of magnitude faster. VB methods have been a
 pplied in such computationally demanding applications as including collabo
 rative filtering\, image and video processing\, NLP and text processing. H
 owever\, despite very nice results in practice\, the theoretical propertie
 s of these approximations are usually not known. In this paper\, we propos
 e a general approach to prove the concentration of variational approximati
 ons of fractional posteriors. We apply our theory to various examples: mat
 rix completion\, Gaussian VB\, nonparametric regression\, mixture models a
 nd other machine learning problems.\n\n\nThis talk is based on joint works
  with James Ridgway\, Nicolas Chopin and Badr-Eddine Chérief-Abdellatif\n
 \nhttp://www.jmlr.org/papers/v17/15-290.html\nhttps://arxiv.org/abs/1706.0
 9293\nhttp://dx.doi.org/doi:10.1214/18-EJS1475\n
LOCATION:MR12
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