Thin-shell stability of Gaussian cooling: logconcave sampling with sesteric complexity from a cold start
Thin-shell stability proof along the Gaussian cooling path improves cold-start logconcave sampling complexity to near n^2.5 from n^2.75.
The authors prove that logconcave probability measures along the Gaussian cooling path have thin-shell stability, generalizing the thin-shell theorem. This yields improved complexity for sampling an arbitrary logconcave distribution from a cold start. For (near-)isotropic logconcave distributions the complexity is nearly n^2.5, improving the previous n^2.75 bound and matching the abstract Speedy walk.
- Generalizes thin-shell theorem to the Gaussian cooling path
- Cold-start logconcave sampling complexity improves from n^2.75 to nearly n^2.5
- Matches the complexity of the abstract Speedy walk
From the original article
1 min read at arxiv.orgWe show that logconcave probability measures along the Gaussian cooling path have thin-shell stability, generalizing the thin-shell theorem. This result leads to improved complexity for the fundamental problem of sampling an arbitrary logconcave distribution from a cold start. For (near-)isotropic logconcave distributions, the complexity is nearly $n^{2.
By Yunbum Kook · arxiv.org
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