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CATEGORIES:Statistics
SUMMARY:Concentration of tempered posteriors and of their 
 variational approximations - Pierre Alquier\, ENSA
 E
DTSTART;TZID=Europe/London:20181116T160000
DTEND;TZID=Europe/London:20181116T170000
UID:TALK109672AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/109672
DESCRIPTION:While Bayesian methods are extremely popular in st
 atistics and machine learning\, their application 
 to massive datasets is often challenging\, when po
 ssible at all. Indeed\, the classical MCMC algorit
 hms are prohibitively slow when both the model dim
 ension and the sample size are large. Variational 
 Bayesian methods aim at approximating the posterio
 r by a distribution in a tractable family. Thus\, 
 MCMC are replaced by an optimization algorithm whi
 ch is orders of magnitude faster. VB methods have 
 been applied in such computationally demanding app
 lications as including collaborative filtering\, i
 mage and video processing\, NLP and text processin
 g. However\, despite very nice results in practice
 \, the theoretical properties of these approximati
 ons are usually not known. In this paper\, we prop
 ose a general approach to prove the concentration 
 of variational approximations of fractional poster
 iors. We apply our theory to various examples: mat
 rix completion\, Gaussian VB\, nonparametric regre
 ssion\, mixture models and other machine learning 
 problems.\n\n\nThis talk is based on joint works w
 ith James Ridgway\, Nicolas Chopin and Badr-Eddine
  Chérief-Abdellatif\n\nhttp://www.jmlr.org/papers/
 v17/15-290.html\nhttps://arxiv.org/abs/1706.09293\
 nhttp://dx.doi.org/doi:10.1214/18-EJS1475\n
LOCATION:MR12
CONTACT:Dr Sergio Bacallado
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