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SUMMARY:Low-rank tensor decompositions for sampling of high-dimensional pr
obability distributions
DTSTART;VALUE=DATE-TIME:20190516T141500
DTEND;VALUE=DATE-TIME:20190516T151500
UID:137b495019baebb95153b3d7f0e66fa2dc7215810d061f8dd3a749cf
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr. Sergey Dolgov (University of Bath\, UK)\nComputational Mat
hematics Seminar\n\nUncertainty quantification and inverse problems in man
y variables are pressingly needed tasks\, yet high-dimensional functions a
re notoriously difficult to integrate in order to compute desired quantiti
es of interest.\nFunctional approximations\, in particular the low-rank se
paration of variables into tensor product decompositions\, have become pop
ular for reducing the computational cost of high-dimensional integration d
own to linear scaling in the number of variables. However\, tensor approxi
mations may be inefficient for non-smooth functions. Sampling based Monte
Carlo methods are more general\, but they may exhibit a very slow converge
nce\, overlooking a hidden structure of the function.\nIn this talk we rev
iew tensor product approximations for the problem of uncertainty quantific
ation and Bayesian inference. This allows efficient integration of smooth
PDE solutions\, posterior density functions and quantities of interest. Mo
reover\, we can use the low-rank approximation of the density function to
construct efficient proposals in the MCMC algorithm for inverse problems.
This combined MCMC method is more accurate also if the quantity of interes
t is not smooth\, such as the indicator function of an event.\n
LOCATION:MA A1 12 https://plan.epfl.ch/?room=MAA112
STATUS:CONFIRMED
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