A stochastic algorithm finding $p$-means on the circle
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ARNAUDON, Marc | |
| hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
| dc.contributor.author | MICLO, Laurent | |
| dc.date.accessioned | 2024-04-04T03:02:05Z | |
| dc.date.available | 2024-04-04T03:02:05Z | |
| dc.date.created | 2013-01-28 | |
| dc.date.issued | 2016-11 | |
| dc.identifier.issn | 1350-7265 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192947 | |
| dc.description.abstractEn | A stochastic algorithm is proposed, finding the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\iy)$. It is fed sequentially with independent random variables $(Y_n)_{n\in\NN}$ distributed according to $\nu$ and this is the only knowledge of $\nu$ required. Furthermore the algorithm is easy to implement, because it evolves like a Brownian motion between the random times it jumps in direction of one of the $Y_n$, $n\in\NN$. Its principle is based on simulated annealing and homogenization, so that temperature and approximations schemes must be tuned up (plus a regularizing scheme if $\nu$ does not admit a Hölderian density). The analyze of the convergence is restricted to the case where the state space is a circle. In its principle, the proof relies on the investigation of the evolution of a time-inhomogeneous $\LL^2$ functional and on the corresponding spectral gap estimates due to Holley, Kusuoka and Stroock. But it requires new estimates on the discrepancies between the unknown instantaneous invariant measures and some convenient Gibbs measures. | |
| dc.language.iso | en | |
| dc.publisher | Bernoulli Society for Mathematical Statistics and Probability | |
| dc.subject.en | spectral gap at small temperature | |
| dc.subject.en | Stochastic algorithms | |
| dc.subject.en | simulated annealing | |
| dc.subject.en | homogenization | |
| dc.subject.en | probability measures on compact Riemannian manifolds | |
| dc.subject.en | intrinsic $p$-means | |
| dc.subject.en | instantaneous invariant measures | |
| dc.subject.en | Gibbs measures | |
| dc.subject.en | spectral gap at small temperature. | |
| dc.subject.en | probability mea-sures on compact Riemannian manifolds | |
| dc.subject.en | intrinsic p-means | |
| dc.title.en | A stochastic algorithm finding $p$-means on the circle | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| bordeaux.journal | Bernoulli | |
| bordeaux.page | 2237-2300 | |
| bordeaux.volume | 22 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00781715 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00781715v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Bernoulli&rft.date=2016-11&rft.volume=22&rft.issue=4&rft.spage=2237-2300&rft.epage=2237-2300&rft.eissn=1350-7265&rft.issn=1350-7265&rft.au=ARNAUDON,%20Marc&MICLO,%20Laurent&rft.genre=article |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||