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SUMMARY:Entropy contraction of the Gibbs sampler under log-concavity - Gia
 como Zanella (Bocconi University)
DTSTART:20241125T142000Z
DTEND:20241125T151000Z
UID:TALK221479@talks.cam.ac.uk
DESCRIPTION:The Gibbs sampler (a.k.a. Glauber dynamics and heat-bath algor
 ithm) is a popular Markov Chain Monte Carlo algorithm which iteratively sa
 mples from the conditional distributions of a probability measure &pi\; of
  interest. Under the assumption that &pi\; is strongly log-concave\, we sh
 ow that the random scan Gibbs sampler contracts in relative entropy and pr
 ovide a sharp characterization of the associated contraction rate. Assumin
 g that evaluating conditionals is cheap compared to evaluating the joint d
 ensity\, our results imply that the number of full evaluations of &pi\; ne
 eded for the Gibbs sampler to mix grows linearly with the condition number
  and is independent of the dimension. If &pi\; is non-strongly log-concave
 \, the convergence rate in entropy degrades from exponential to polynomial
 . Our techniques are versatile and extend to Metropolis-within-Gibbs schem
 es and the Hit-and-Run algorithm. A comparison with gradient-based schemes
  and the connection with the optimization literature are also discussed. T
 his is joint work with Filippo Ascolani and Hugo Lavenant.
LOCATION:Seminar Room 1\, Newton Institute
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