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DTSTART:20221030T030000
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UID:calendar.130852.field_date.0@www.tse-fr.eu
DTSTAMP:20230401T192617Z
CREATED:20230216T151001Z
DESCRIPTION:Mikolaj Kasprzak (University of Luxembourg)\, “How good is your
Laplace approximation of the Bayesian posterior? Finite-sample error boun
ds for a variety of useful divergences”\, Maths Job Market Seminar\, TSE\,
Toulouse\, March 20\, 2023\, 09:30–10:45\, Auditorium A3.\n\nThe Laplace
approximation is a popular method for obtaining estimates of intractable e
xpectations with respect to Bayesian posteriors. But can we trust these es
timates for practical use? A theoretical justification for this method com
es from the Bernstein - von Mises Theorem\, also known as the Bayesian Cen
tral Limit Theorem (BCLT)\, which gives conditions under which the posteri
or looks asymptotically Gaussian. One might\, therefore\, consider using r
ate-of-convergence bounds for the BCLT to construct non-asymptotic quality
guarantees for the Laplace approximation. But the bounds in the existing
versions of the BCLT either: require knowing the true data-generating para
meter\, are asymptotic in the number of samples\, do not control the poste
rior mean and variance\, or apply only to narrow classes of models. Such b
ounds are therefore of limited use in real-life applications. Our work pro
vides the first closed-form\, finite-sample quality bounds for the Laplace
approximation that simultaneously (1) do not require knowing the true par
ameter\, (2) control posterior means and variances\, (3) control a variety
of distances that metrize weak convergence and (4) apply generally to mod
els that satisfy the conditions of the asymptotic BCLT. In fact\, our boun
ds work even in the presence of misspecification. We compute exact constan
ts in our bounds for a variety of standard models\, including logistic reg
ression\, and numerically demonstrate their utility. We also provide a fra
mework for the analysis of more complex models. Among the technical tools
we use are Stein's method and the log-Sobolev inequality.
DTSTART;TZID=Europe/Paris:20230320T093000
DTEND;TZID=Europe/Paris:20230320T104500
LAST-MODIFIED:20230307T011002Z
LOCATION:TSE\, Toulouse\, March 20\, 2023\, 09:30–10:45\, Auditorium A3
SUMMARY:Maths Job Market Seminar
URL;TYPE=URI:https://www.tse-fr.eu/seminars/2023-how-good-your-laplace-appr
oximation-bayesian-posterior-finite-sample-error-bounds-variety-useful
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