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SUMMARY:Generative models and Bayesian inversion using Laplace approximati
on
DTSTART;VALUE=DATE-TIME:20220628T093000Z
DTEND;VALUE=DATE-TIME:20220628T095000Z
DTSTAMP;VALUE=DATE-TIME:20220930T152311Z
UID:indico-contribution-253@conferences.enbis.org
DESCRIPTION:Speakers: Manuel Marschall (Physikalisch-Technische Bundesanst
alt)\nSolving inverse problems with the Bayesian paradigm relies on a sens
ible choice of the prior. Elicitation of expert knowledge and formulation
of physical constraints in a probabilistic sense is often challenging. Rec
ently\, the advances made in machine leaning and statistical generative mo
dels have been used to develop novel approaches to Bayesian inference rely
ing on data-driven and highly informative priors. A generative model is ab
le to synthesize new data that resemble the properties of a given data set
. Famous examples comprise the generation of high-quality images of faces
from people that do not exist. For the inverse problem\, the underlying da
ta set should reflect the properties of the sought solution\, such as typi
cal structures of the tissue in the human brain in MR imaging. Such a data
distribution can often be assumed to be embedded in a low dimensional man
ifold of the original data space. Typically\, the inference is carried out
in the manifold determined by the generative model\, since the lower dime
nsionality favors the optimization. However\, this proceeding lacks import
ant statistical aspects\, such as the existence of a posterior probability
density function or the consistency of Bayes estimators. Therefore\, we e
xplore an alternative approach for Bayesian inference in the original high
dimensional space based on probabilistic generative models that admit the
aforementioned properties. In addition\, based on a Laplace approximation
\, the posterior can be estimated numerically efficient and for linear Gau
ssian models even analytically. We perform numerical experiments on typica
l data sets from machine learning and confirm our theoretical findings. In
conjunction with our asymptotic analysis\, a heuristic guidance on the ch
oice of the method is presented.\n\nhttps://conferences.enbis.org/event/18
/contributions/253/
LOCATION: EL6
URL:https://conferences.enbis.org/event/18/contributions/253/
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