Essec\Faculty\Model\Contribution {#2216 ▼
#_index: "academ_contributions"
#_id: "10689"
#_source: array:26 [
"id" => "10689"
"slug" => "10689-network-models-and-sparse-graphon-estimation"
"yearMonth" => "2018-06"
"year" => "2018"
"title" => "Network models and sparse graphon estimation."
"description" => "KLOPP, O., TSYBAKOV, A. et VERZELEN, N. (2018). Network models and sparse graphon estimation. Dans: NordStat 2018. Tartu. 
KLOPP, O., TSYBAKOV, A. et VERZELEN, N. (2018). Network models and sparse graphon estimation. Dans: "
"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" => "NordStat 2018"
"keywords" => array:6 [
0 => "inhomogeneous random graph"
1 => "networks"
2 => "oracle inequality"
3 => """
sparse\n
graphon
"""
4 => "sparsity"
5 => "stochastic block model"
]
"updatedAt" => "2021-09-24 10:33:27"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => null
"volume" => null
"number" => null
]
"type" => array:2 [
"fr" => "Communications dans une conférence"
"en" => "Presentations at an Academic or Professional conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => """
Inhomogeneous random graph models encompass many network models such as\n
stochastic block models and latent position models. We consider the problem of\n
statistical estimation of the matrix of connection probabilities based on the obser-\n
vations of the adjacency matrix of the network. Taking the stochastic block model\n
as an approximation, we construct estimators of network connection probabilities –\n
the ordinary block constant least squares estimator, and its restricted version. We\n
show that they satisfy oracle inequalities with respect to the block constant oracle.\n
As a consequence, we derive optimal rates of estimation of the probability matrix.\n
Our results cover the important setting of sparse networks. Another consequence\n
consists in establishing upper bounds on the minimax risks for graphon estimation\n
in the L 2 norm when the probability matrix is sampled according to a graphon\n
model. These bounds include an additional term accounting for the “agnostic”\n
error induced by the variability of the latent unobserved variables of the graphon\n
model. In this setting, the optimal rates are influenced not only by the bias and\n
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\n
between estimation under the empirical loss (the probability matrix estimation) and\n
under the integrated loss (the graphon estimation).
"""
"en" => """
Inhomogeneous random graph models encompass many network models such as\n
stochastic block models and latent position models. We consider the problem of\n
statistical estimation of the matrix of connection probabilities based on the obser-\n
vations of the adjacency matrix of the network. Taking the stochastic block model\n
as an approximation, we construct estimators of network connection probabilities –\n
the ordinary block constant least squares estimator, and its restricted version. We\n
show that they satisfy oracle inequalities with respect to the block constant oracle.\n
As a consequence, we derive optimal rates of estimation of the probability matrix.\n
Our results cover the important setting of sparse networks. Another consequence\n
consists in establishing upper bounds on the minimax risks for graphon estimation\n
in the L 2 norm when the probability matrix is sampled according to a graphon\n
model. These bounds include an additional term accounting for the “agnostic”\n
error induced by the variability of the latent unobserved variables of the graphon\n
model. In this setting, the optimal rates are influenced not only by the bias and\n
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\n
between estimation under the empirical loss (the probability matrix estimation) and\n
under the integrated loss (the graphon 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" => "Network models and sparse graphon estimation."
"docSurtitle" => "Presentations at an Academic or Professional conference"
"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">2018</span> <span class="document-property-authors">KLOPP Olga, TSYBAKOV Alexandre, VERZELEN Nicolas</span><br>< "
"keywordList" => """
<a href="#">inhomogeneous random graph</a>, <a href="#">networks</a>, <a href="#">oracle inequality</a>, <a href="#">sparse\n <a href="#">inhomogeneous random graph</a>, <a href="#">networks</a>, <a href="#">oracle inequality<
graphon</a>, <a href="#">sparsity</a>, <a href="#">stochastic block model</a>
"""
"docPreview" => "<b>Network models and sparse graphon estimation.</b><br><span>2018-06 | Presentations at an Academic or Professional conference </span> <b>Network models and sparse graphon estimation.</b><br><span>2018-06 | Presentations at an Academic "
"docType" => "research"
"publicationLink" => "<a href="#" target="_blank">Network models and sparse graphon estimation.</a>"
]
+lang: "en"
+"_type": "_doc"
+"_score": 8.754634
+"parent": null
}
