English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We analyze the complexity of sampling from a class of heavy-taileddistributions by discretizing a natural class of It\^o diffusions associatedwith weighted Poincar\'e inequalities. Based on a mean-square analysis, weestablish the iteration complexity for obtaining a sample whose distribution is$\epsilon$ close to the target distribution in the Wasserstein-2 metric. Inthis paper, our results take the mean-square analysis to its limits, i.e., weinvariably only require that the target density has finite variance, theminimal requirement for a mean-square analysis. To obtain explicit estimates,we compute upper bounds on certain moments associated with heavy-tailed targetsunder various assumptions. We also provide similar iteration complexity resultsfor the case where only function evaluations of the unnormalized target densityare available by estimating the gradients using a Gaussian smoothing technique.We provide illustrative examples based on the multivariate $t$-distribution.

Mean-Square Analysis of Discretized It\^o Diffusions for Heavy-tailed Sampling