Risk estimation for matrix recovery with spectral regularization
| hal.structure.identifier | CEntre de REcherches en MAthématiques de la DEcision [CEREMADE] | |
| dc.contributor.author | DELEDALLE, Charles-Alban | |
| hal.structure.identifier | CEntre de REcherches en MAthématiques de la DEcision [CEREMADE] | |
| dc.contributor.author | VAITER, Samuel | |
| hal.structure.identifier | CEntre de REcherches en MAthématiques de la DEcision [CEREMADE] | |
| dc.contributor.author | PEYRÉ, Gabriel | |
| hal.structure.identifier | Equipe Image - Laboratoire GREYC - UMR6072 | |
| dc.contributor.author | FADILI, Jalal M. | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DOSSAL, Charles | |
| dc.date.accessioned | 2024-04-04T02:24:20Z | |
| dc.date.available | 2024-04-04T02:24:20Z | |
| dc.date.created | 2012-05-07 | |
| dc.date.conference | 2012-06-30 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189811 | |
| dc.description.abstractEn | In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of the SURE theory, a key step is to compute the (weak) derivative and divergence of a solution with respect to the observations. As such a solution is not available in closed form, but rather through a proximal splitting algorithm, we propose to recursively compute the divergence from the sequence of iterates. A second challenge that we unlocked is the computation of the (weak) derivative of the proximity operator of a spectral function. To show the potential applicability of our approach, we exemplify it on a matrix completion problem to objectively and automatically select the regularization parameter. | |
| dc.language.iso | en | |
| dc.subject.en | Risk estimation | |
| dc.subject.en | SURE | |
| dc.subject.en | matrix recovery | |
| dc.subject.en | matrix completion | |
| dc.subject.en | matrix-valued function | |
| dc.subject.en | spectral regularization | |
| dc.subject.en | nuclear norm | |
| dc.subject.en | proximal algorithms | |
| dc.title.en | Risk estimation for matrix recovery with spectral regularization | |
| dc.type | Communication dans un congrès | |
| dc.subject.hal | Mathématiques [math]/Statistiques [math.ST] | |
| dc.subject.hal | Mathématiques [math]/Théorie de l'information et codage [math.IT] | |
| dc.subject.hal | Informatique [cs]/Apprentissage [cs.LG] | |
| dc.subject.hal | Informatique [cs]/Traitement du signal et de l'image | |
| dc.subject.hal | Informatique [cs]/Théorie de l'information [cs.IT] | |
| dc.subject.hal | Statistiques [stat]/Machine Learning [stat.ML] | |
| dc.subject.hal | Statistiques [stat]/Théorie [stat.TH] | |
| dc.subject.hal | Sciences de l'ingénieur [physics]/Traitement du signal et de l'image | |
| dc.identifier.arxiv | 1205.1482 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.conference.title | ICML'2012 workshop on Sparsity, Dictionaries and Projections in Machine Learning and Signal Processing | |
| bordeaux.country | GB | |
| bordeaux.conference.city | Edinburgh | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00695326 | |
| hal.version | 1 | |
| hal.invited | non | |
| hal.proceedings | non | |
| hal.conference.end | 2012-07-01 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00695326v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=DELEDALLE,%20Charles-Alban&VAITER,%20Samuel&PEYR%C3%89,%20Gabriel&FADILI,%20Jalal%20M.&DOSSAL,%20Charles&rft.genre=unknown |
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