Essec\Faculty\Model\Contribution {#2188
#_index: "academ_contributions"
#_id: "13901"
#_source: array:26 [
"id" => "13901"
"slug" => "a-bayesian-approach-for-noisy-matrix-completion-optimal-rate-under-general-sampling-distribution"
"yearMonth" => "2015-04"
"year" => "2015"
"title" => "A Bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution"
"description" => "MAI, T.T. et ALQUIER, P. (2015). A Bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution. <i>The Electronic Journal of Statistics</i>, 9(1), pp. 823-841."
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "MAI The Tien"
]
]
"ouvrage" => ""
"keywords" => array:6 [
0 => "Matrix completion"
1 => "Bayesian Analysis"
2 => "PACBayesian bounds"
3 => "oracle inequality"
4 => "low-rank matrix"
5 => "Gibbs sampler"
]
"updatedAt" => "2023-03-22 10:04:50"
"publicationUrl" => "https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-9/issue-1/A-Bayesian-approach-for-noisy-matrix-completion--Optimal-rate/10.1214/15-EJS1020.full"
"publicationInfo" => array:3 [
"pages" => "823-841"
"volume" => "9"
"number" => "1"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally [3, 18, 19, 24, 28]. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of view (see [7, 9, 16, 23] among others) in this problem, the theoretical optimality of Bayesian estimators have not been explored yet. In this paper, we propose a Bayesian estimator for matrix completion under general sampling distribution. We also provide an oracle inequality for this estimator. This inequality proves that, whatever the rank of the matrix to be estimated, our estimator reaches the minimax-optimal rate of convergence (up to a logarithmic factor). We end the paper with a short simulation study."
"en" => "Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally [3, 18, 19, 24, 28]. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of view (see [7, 9, 16, 23] among others) in this problem, the theoretical optimality of Bayesian estimators have not been explored yet. In this paper, we propose a Bayesian estimator for matrix completion under general sampling distribution. We also provide an oracle inequality for this estimator. This inequality proves that, whatever the rank of the matrix to be estimated, our estimator reaches the minimax-optimal rate of convergence (up to a logarithmic factor). We end the paper with a short simulation study."
]
"authors_fields" => array:2 [
"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-04-26T05:21:53.000Z"
"docTitle" => "A Bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution"
"docSurtitle" => "Journal articles"
"authorNames" => "<a href="/cv/alquier-pierre">ALQUIER Pierre</a>, MAI The Tien"
"docDescription" => "<span class="document-property-authors">ALQUIER Pierre, MAI The Tien</span><br><span class="document-property-authors_fields">Information Systems, Decision Sciences and Statistics</span> | <span class="document-property-year">2015</span>"
"keywordList" => "<a href="#">Matrix completion</a>, <a href="#">Bayesian Analysis</a>, <a href="#">PACBayesian bounds</a>, <a href="#">oracle inequality</a>, <a href="#">low-rank matrix</a>, <a href="#">Gibbs sampler</a>"
"docPreview" => "<b>A Bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution</b><br><span>2015-04 | Journal articles </span>"
"docType" => "research"
"publicationLink" => "<a href="https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-9/issue-1/A-Bayesian-approach-for-noisy-matrix-completion--Optimal-rate/10.1214/15-EJS1020.full" target="_blank">A Bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution</a>"
]
+lang: "en"
+"_type": "_doc"
+"_score": 8.550009
+"parent": null
}
