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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
ChÃ©rief-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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