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SUMMARY:Sampling from multi-modal distributions via stochastic localizatio
 n - Maxence Noble-Bourillot (Ecole Polytechnique Paris)
DTSTART:20240704T120000Z
DTEND:20240704T133000Z
UID:TALK217951@talks.cam.ac.uk
DESCRIPTION:Building upon score-based learning\, new interest in stochasti
 c localization techniques has recently emerged. In these models\, one seek
 s to noise a sample from the data distribution through a stochastic proces
 s\, called observation process\, and progressively learns a denoiser assoc
 iated to this dynamics. Apart from specific applications\, the use of stoc
 hastic localization for the problem of sampling from an unnormalized targe
 t density has not been explored extensively. This work contributes to fill
  this gap. We consider a general stochastic localization framework and int
 roduce an explicit class of observation processes\, associated with flexib
 le denoising schedules. We provide a complete methodology\, Stochastic Loc
 alization via Iterative Posterior Sampling (SLIPS)\, to obtain approximate
  samples of this dynamics\, and as a by-product\, samples from the target 
 distribution. Our scheme is based on a Markov chain Monte Carlo estimation
  of the denoiser and comes with detailed practical guidelines. We highligh
 t the bridge with recent methods built upon denoising models such as stoch
 astic interpolants and diffusion models. Finally\, we illustrate the benef
 its and applicability of SLIPS on several benchmarks of multi-modal distri
 butions\, including Gaussian mixtures in increasing dimensions\, Bayesian 
 logistic regression and a high-dimensional field system from statistical-m
 echanics.&nbsp\;
LOCATION:External
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