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SUMMARY:Regularized Dikin Walks for Sampling Truncated Logconcave Measures
 \, Mixed Isoperimetry and Beyond Worst-Case Analysis [Oberseminar Stochast
 ics]
DTSTART:20250508T143000Z
DTEND:20250508T153000Z
DTSTAMP:20260416T082200Z
UID:indico-event-386@math-events.uni-bonn.de
DESCRIPTION:Speakers: Yuansi Chen (ETH Zürich)\n\nWe study the problem of
  drawing samples from a logconcave distribution truncated on a polytope\, 
 motivated by computational challenges in Bayesian statistical models with 
 indicator variables\, such as probit regression. Building on interior poin
 t methods and the Dikin walk for sampling from uniform distributions\, we 
 analyze the mixing time of regularized Dikin walks. For a logconcave and l
 og-smooth distribution with condition number $\\kappa$\, truncated on a po
 lytope in $R^n$ defined with $m$ linear constraints\, we prove that the so
 ft-threshold Dikin walk mixes in $O((m+\\kappa)n)$ iterations from a warm 
 initialization. It improves upon prior work which required the polytope to
  be bounded and involved a bound dependent on the radius of the bounded re
 gion. Going beyond worst-case mixing time analysis\, we demonstrate that t
 he soft-threshold Dikin walk can mix significantly faster when only a limi
 ted number of constraints intersect the high-probability mass of the distr
 ibution\, improving the $O((m+\\kappa)n)$ upper bound to $O(m + \\kappa n)
 $.\n \narXiv link: https://arxiv.org/abs/2412.11303\n \n\nhttps://math-e
 vents.uni-bonn.de/event/386/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/386/
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