@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00809487v1> a dcat:Dataset ;
    dct:description """
              It is the goal of this paper to extend the \\textit{Empirical Risk Minimization} (ERM) paradigm, from a practical perspective, to the situation where a natural estimate of the risk is of the form of a $K$-sample $U$-statistics, as it is the case in the $K$-partite ranking problem for instance. Indeed, the numerical computation of the empirical risk is hardly feasible if not infeasible, even for moderate samples sizes. Precisely, it involves averaging $O(n^{d_1+\\ldots+d_K})$ terms, when considering a $U$-statistic of degrees $(d_1,\\;\\ldots,\\; d_K)$ based on samples of sizes proportional to $n$. We propose here to consider a drastically simpler Monte-Carlo version of the empirical risk based on $O(n)$ terms solely, which can be viewed as an \\textit{incomplete generalized $U$-statistic}, and prove that, remarkably, the approximation stage does not damage the ERM procedure and yields a learning rate of order $O_{\\mathbb{P}}(1/\\sqrt{n})$. Beyond a theoretical analysis guaranteeing the validity of this approach, numerical experiments are displayed for illustrative purpose.
            """ ;
    dct:identifier "hal-00809487" ;
    dct:issued "2026-05-11T15:20:40.680449"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-11T15:20:40.680454"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Maximal Deviations of Incomplete U-statistics with Applications to Empirical Risk Sampling" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00809487v1/resource/0084333c-9171-4107-9442-25a4eaded2d5> ;
    dcat:keyword "empirical-risk-minimization",
        "incomplete-u-statistics",
        "infoeu-reposemanticspreprint",
        "minimum-volume-set",
        "preprints-working-papers-",
        "ranking",
        "risk-sampling",
        "statmlstatistics-statmachine-learning-statml" ;
    dcat:landingPage <https://hal.science/hal-00809487> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00809487v1/resource/0084333c-9171-4107-9442-25a4eaded2d5> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-11T15:20:40.700537"^^xsd:dateTime ;
    dct:modified "2026-05-11T15:20:40.666731"^^xsd:dateTime ;
    dct:title "Maximal Deviations of Incomplete U-statistics with Applications to Empirical Risk Sampling" ;
    dcat:accessURL <https://hal.science/hal-00809487> .

<https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> a foaf:Agent ;
    foaf:name "test_moissonnage_selune" .

<https://hal.science/hal-00809487> a foaf:Document .