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SUMMARY:Optimization-Based Uncertainty Quantification for Ill-Posed Invers
 e Problems
DTSTART:20211119T151500
DTEND:20211119T170000
DTSTAMP:20260407T081747Z
UID:6cbf60469e73e7d425bcf5af49fd6b5397daf0ba4fa6ec5902727fd7
CATEGORIES:Conferences - Seminars
DESCRIPTION:Mikael Kuusela\, Department of Statistics and Data Science\, C
 arnegie Mellon University\nIll-posed inverse problems are situations where
  inferring the quantity of interest based on noisy data tends to produce e
 xtremely unstable solutions. It is customary to address this using regular
 ization which reduces the variance of the estimates at the expense of an i
 ncreased bias. While this can lead to well-behaved point estimates\, it is
  challenging to provide rigorous frequentist uncertainties for the regular
 ized estimates. In this talk\, I will describe approaches that can be used
  to obtain improved frequentist uncertainty quantification in ill-posed pr
 oblems.\nThe common theme of these methods is that they avoid explicit reg
 ularization by optimizing confidence bounds on functionals of the unknown 
 quantity which implicitly regularizes the problem. This yields well-calibr
 ated finite-sample frequentist uncertainties even in rank-deficient proble
 ms and in the presence of constraints. Special focus will be given to a ne
 w decision-theoretic approach for constructing such confidence bounds. Thr
 oughout this talk\, I will demonstrate these ideas using case studies from
  particle physics and atmospheric remote sensing.\n 
LOCATION:https://epfl.zoom.us/j/65553788434
STATUS:CONFIRMED
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