Theoretical guarantees for neural control variates in MCMC
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912088595628032 |
|---|---|
| author | Belomestny, Denis Goldman, Artur Naumov, Alexey Samsonov, Sergey |
| author_facet | Belomestny, Denis Goldman, Artur Naumov, Alexey Samsonov, Sergey |
| contents | In this paper, we propose a variance reduction approach for Markov chains based on additive control variates and the minimization of an appropriate estimate for the asymptotic variance. We focus on the particular case when control variates are represented as deep neural networks. We derive the optimal convergence rate of the asymptotic variance under various ergodicity assumptions on the underlying Markov chain. The proposed approach relies upon recent results on the stochastic errors of variance reduction algorithms and function approximation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01111 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Theoretical guarantees for neural control variates in MCMC Belomestny, Denis Goldman, Artur Naumov, Alexey Samsonov, Sergey Statistics Theory Machine Learning Probability Methodology 65C40, 62-08 In this paper, we propose a variance reduction approach for Markov chains based on additive control variates and the minimization of an appropriate estimate for the asymptotic variance. We focus on the particular case when control variates are represented as deep neural networks. We derive the optimal convergence rate of the asymptotic variance under various ergodicity assumptions on the underlying Markov chain. The proposed approach relies upon recent results on the stochastic errors of variance reduction algorithms and function approximation theory. |
| title | Theoretical guarantees for neural control variates in MCMC |
| topic | Statistics Theory Machine Learning Probability Methodology 65C40, 62-08 |
| url | https://arxiv.org/abs/2304.01111 |