Essec\Faculty\Model\Contribution {#2216 ▼
#_index: "academ_contributions"
#_id: "10678"
#_source: array:26 [
"id" => "10678"
"slug" => "10678-oracle-inequalities-for-network-models-and-sparse-graphon-estimation"
"yearMonth" => "2017-02"
"year" => "2017"
"title" => "Oracle inequalities for network models and sparse graphon estimation"
"description" => "KLOPP, O., TSYBAKOV, A. et VERZELEN, N. (2017). Oracle inequalities for network models and sparse graphon estimation. <i>Annals of Statistics</i>, 45(1), pp. 316-354. 
KLOPP, O., TSYBAKOV, A. et VERZELEN, N. (2017). Oracle inequalities for network models and sparse gr "
"authors" => array:3 [
0 => array:3 [
"name" => "KLOPP Olga"
"bid" => "B00732676"
"slug" => "klopp-olga"
]
1 => array:1 [
"name" => "TSYBAKOV Alexandre"
]
2 => array:1 [
"name" => "VERZELEN Nicolas"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2021-09-24 10:33:27"
"publicationUrl" => "https://hal.archives-ouvertes.fr/hal-01176210/document"
"publicationInfo" => array:3 [
"pages" => "316-354"
"volume" => "45"
"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" => """
Inhomogeneous random graph models encompass many network models such as stochastic block\n
models and latent position models. We consider the problem of statistical estimation of the matrix of\n models and latent position models. We consider the problem of statistical estimation of the matrix o
connection probabilities based on the observations of the adjacency matrix of the network. Taking the\n connection probabilities based on the observations of the adjacency matrix of the network. Taking th
stochastic block model as an approximation, we construct estimators of network connection probabilities\n stochastic block model as an approximation, we construct estimators of network connection probabilit
– the ordinary block constant least squares estimator, and its restricted version. We show that they\n – the ordinary block constant least squares estimator, and its restricted version. We show that they
satisfy oracle inequalities with respect to the block constant oracle. As a consequence, we derive optimal\n satisfy oracle inequalities with respect to the block constant oracle. As a consequence, we derive o
rates of estimation of the probability matrix. Our results cover the important setting of sparse networks.\n rates of estimation of the probability matrix. Our results cover the important setting of sparse net
Another consequence consists in establishing upper bounds on the minimax risks for graphon estimation\n Another consequence consists in establishing upper bounds on the minimax risks for graphon estimatio
in the L2 norm when the probability matrix is sampled according to a graphon model. These bounds\n
include an additional term accounting for the “agnostic” error induced by the variability of the latent\n include an additional term accounting for the “agnostic” error induced by the variability of the lat
unobserved variables of the graphon model. In this setting, the optimal rates are influenced not only\n unobserved variables of the graphon model. In this setting, the optimal rates are influenced not onl
by the bias and variance components as in usual nonparametric problems but also include the third\n
component, which is the agnostic error. The results shed light on the differences between estimation\n component, which is the agnostic error. The results shed light on the differences between estimation
under the empirical loss (the probability matrix estimation) and under the integrated loss (the graphon\n under the empirical loss (the probability matrix estimation) and under the integrated loss (the grap
estimation).
"""
"en" => """
Inhomogeneous random graph models encompass many network models such as stochastic block\n
models and latent position models. We consider the problem of statistical estimation of the matrix of\n models and latent position models. We consider the problem of statistical estimation of the matrix o
connection probabilities based on the observations of the adjacency matrix of the network. Taking the\n connection probabilities based on the observations of the adjacency matrix of the network. Taking th
stochastic block model as an approximation, we construct estimators of network connection probabilities\n stochastic block model as an approximation, we construct estimators of network connection probabilit
– the ordinary block constant least squares estimator, and its restricted version. We show that they\n – the ordinary block constant least squares estimator, and its restricted version. We show that they
satisfy oracle inequalities with respect to the block constant oracle. As a consequence, we derive optimal\n satisfy oracle inequalities with respect to the block constant oracle. As a consequence, we derive o
rates of estimation of the probability matrix. Our results cover the important setting of sparse networks.\n rates of estimation of the probability matrix. Our results cover the important setting of sparse net
Another consequence consists in establishing upper bounds on the minimax risks for graphon estimation\n Another consequence consists in establishing upper bounds on the minimax risks for graphon estimatio
in the L2 norm when the probability matrix is sampled according to a graphon model. These bounds\n
include an additional term accounting for the “agnostic” error induced by the variability of the latent\n include an additional term accounting for the “agnostic” error induced by the variability of the lat
unobserved variables of the graphon model. In this setting, the optimal rates are influenced not only\n unobserved variables of the graphon model. In this setting, the optimal rates are influenced not onl
by the bias and variance components as in usual nonparametric problems but also include the third\n
component, which is the agnostic error. The results shed light on the differences between estimation\n component, which is the agnostic error. The results shed light on the differences between estimation
under the empirical loss (the probability matrix estimation) and under the integrated loss (the graphon\n under the empirical loss (the probability matrix estimation) and under the integrated loss (the grap
estimation).
"""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-12T03:21:41.000Z"
"docTitle" => "Oracle inequalities for network models and sparse graphon estimation"
"docSurtitle" => "Journal articles"
"authorNames" => "<a href="/cv/klopp-olga">KLOPP Olga</a>, TSYBAKOV Alexandre, VERZELEN Nicolas"
"docDescription" => "<span class="document-property-authors">KLOPP Olga, TSYBAKOV Alexandre, VERZELEN Nicolas</span><br><span class="document-property-authors_fields">Information Systems, Data Analytics and Operations</span> | <span class="document-property-year">2017</span> <span class="document-property-authors">KLOPP Olga, TSYBAKOV Alexandre, VERZELEN Nicolas</span><br>< "
"keywordList" => ""
"docPreview" => "<b>Oracle inequalities for network models and sparse graphon estimation</b><br><span>2017-02 | Journal articles </span> <b>Oracle inequalities for network models and sparse graphon estimation</b><br><span>2017-02 | Journ "
"docType" => "research"
"publicationLink" => "<a href="https://hal.archives-ouvertes.fr/hal-01176210/document" target="_blank">Oracle inequalities for network models and sparse graphon estimation</a> <a href="https://hal.archives-ouvertes.fr/hal-01176210/document" target="_blank">Oracle inequalities "
]
+lang: "en"
+"_type": "_doc"
+"_score": 8.674879
+"parent": null
}
