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SUMMARY:A high-probability mixing time bound for Gibbs sampling from log-s
 mooth strongly log-concave distributions - Neha Spenta Wadia (Simons Found
 ation)
DTSTART:20241204T150000Z
DTEND:20241204T160000Z
UID:TALK224266@talks.cam.ac.uk
DESCRIPTION:Markov Chain Monte Carlo (MCMC) is a simple\, generic strategy
  for sampling from a probability distribution $\\pi(x)$\, $x\\in\\mathbb{R
 }^n$\, in any dimension $n$. The Gibbs sampler is the natural MCMC algorit
 hm to use when the one-dimensional full conditional distributions of each 
 coordinate $x_i$ of $x$ are known and easy to sample from. Although an asy
 mptotic guarantee of convergence for this sampler has existed for some tim
 e\, non-asymptotic guarantees that identify the dimension dependence of it
 s convergence behavior have only just begun to emerge. Building on the rec
 ent work of Aditi Laddha and Santosh Vempala\, in which they establish a m
 ixing time bound for Gibbs sampling from a uniform distribution supported 
 on a convex body that is polynomial in $n$\, we present a high-probability
  mixing time bound for the same sampler for log-smooth and strongly log-co
 ncave distributions supported on $\\mathbb{R}^n$. This bound is also polyn
 omial in $n$ up to logarithmic factors. Its proof proceeds via a conductan
 ce argument and relies on a new high-probability $L_0$ isoperimetric inequ
 ality for subsets of a convex body.
LOCATION:Seminar Room 2\, Newton Institute
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