Sampling, Diffusions, and Stochastic Localization
- URL: http://arxiv.org/abs/2305.10690v1
- Date: Thu, 18 May 2023 04:01:40 GMT
- Title: Sampling, Diffusions, and Stochastic Localization
- Authors: Andrea Montanari
- Abstract summary: Diffusions are a successful technique to sample from high-dimensional distributions.
localization is a technique to prove mixing of Markov Chains and other functional inequalities in high dimension.
An algorithmic version of localization was introduced in [EAMS2022] to obtain an algorithm that samples from certain statistical mechanics models.
- Score: 10.368585938419619
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Diffusions are a successful technique to sample from high-dimensional
distributions can be either explicitly given or learnt from a collection of
samples. They implement a diffusion process whose endpoint is a sample from the
target distribution and whose drift is typically represented as a neural
network. Stochastic localization is a successful technique to prove mixing of
Markov Chains and other functional inequalities in high dimension. An
algorithmic version of stochastic localization was introduced in [EAMS2022], to
obtain an algorithm that samples from certain statistical mechanics models.
This notes have three objectives: (i) Generalize the construction [EAMS2022]
to other stochastic localization processes; (ii) Clarify the connection between
diffusions and stochastic localization. In particular we show that standard
denoising diffusions are stochastic localizations but other examples that are
naturally suggested by the proposed viewpoint; (iii) Describe some insights
that follow from this viewpoint.
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