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              <p>Le problème de minimisation du risque empirique (ERM) avec régularisation d'entropie relative (ERM-RER) est étudié sous l'hypothèse que la mesure de référence est une mesure $\sigma$-finie, et pas nécessairement une mesure de probabilité. Sous cette hypothèse, qui conduit à une généralisation du problème ERM-RER permettant une plus grande flexibilité pour l'incorporation des connaissances antérieures, de nombreuses propriétés pertinentes sont énoncées. Parmi ces propriétés, la solution à ce problème, si elle existe, se révèle être une mesure de probabilité unique,  mutuellement absolument continue avec la mesure de référence. Une telle solution présente une garantie probablement-approximativement-correcte pour le problème ERM indépendamment du fait que ce dernier possède ou non une solution. Pour un ensemble de données fixe, et sous une condition particulière, le risque empirique s'avère être une variable aléatoire sous-gaussienne lorsque les modèles sont échantillonnés à partir de la solution au problème ERM-RER. Les capacités de généralisation de la solution au problème ERM-RER (l'algorithme de Gibbs) sont étudiées via la sensibilité de la valeur espérée du risque empirique aux déviations d'une telle solution vers des mesures de probabilité alternatives. Enfin, un lien intéressant entre la sensibilité, l'erreur de généralisation et l'information lautum est établi.</p>
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        <org type="institution" xml:id="struct-73928" status="VALID">
          <orgName>National Chiao Tung University</orgName>
          <orgName type="acronym">NCTU</orgName>
          <desc>
            <address>
              <addrLine>1001 University Road, Hsinchu, Taiwan 300, ROC</addrLine>
              <country key="TW"/>
            </address>
            <ref type="url">http://www.nctu.edu.tw/english/index.php</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>