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SUMMARY:Polynomial time guarantees for sampling based posterior inference 
 - Randolf Altmeyer (Imperial College London)
DTSTART:20241128T142000Z
DTEND:20241128T151000Z
UID:TALK221560@talks.cam.ac.uk
DESCRIPTION:The Bayesian approach provides a flexible framework for a wide
  range of non-parametric inference problems. It crucially relies on comput
 ing functionals with respect to the posterior distribution\, such as the p
 osterior mean or posterior quantiles for uncertainty quantification. Since
  the posterior is rarely available in closed form\, inference is based on 
 Markov chain Monte Carlo (MCMC) sampling algorithms. The runtime of these 
 algorithms until a given target precision is achieved will typically scale
  exponentially in the model dimension and the sample size. In contrast\, i
 n this talk we will see that sampling based posterior inference in a gener
 al high-dimensional setup is feasible\, even without global structural ass
 umptions such as strong log-concavity of the posterior. Given a sufficient
 ly good initialiser\, we present polynomial-time convergence guarantees fo
 r a widely used gradient based MCMC sampling scheme. The key idea is to co
 mbine posterior contraction with the local curvature induced by the Fisher
 -information of the statistical model near the data generating truth. We w
 ill discuss applications to high-dimensional logistic and Gaussian regress
 ion\, as well as to density estimation.
LOCATION:Seminar Room 1\, Newton Institute
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