| Autor: |
Andrieu, Christophe, Lee, Anthony, Power, Sam, Wang, Andi Q. |
| Rok vydání: |
2023 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
We investigate the application of Weak Poincar\'e Inequalities (WPI) to Markov chains to study their rates of convergence and to derive complexity bounds. At a theoretical level we investigate the necessity of the existence of WPIs to ensure \mathrm{L}^{2}-convergence, in particular by establishing equivalence with the Resolvent Uniform Positivity-Improving (RUPI) condition and providing a counterexample. From a more practical perspective, we extend the celebrated Cheeger's inequalities to the subgeometric setting, and further apply these techniques to study random-walk Metropolis algorithms for heavy-tailed target distributions and to obtain lower bounds on pseudo-marginal algorithms. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
