Document Zbl 1105.62353

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Stat.</a> <a href="/?q=in%3A104859" title="Articles in this Issue">32, No. 1, 135-166 (2004)</a>. </div> <div class="abstract">Summary: Classification can be considered as nonparametric estimation of sets, where the risk is defined by means of a specific distance between sets associated with misclassification error. It is shown that the rates of convergence of classifiers depend on two parameters: the complexity of the class of candidate sets and the margin parameter. The dependence is explicitly given, indicating that optimal fast rates approaching $O(n^{-1})$ can be attained, where n is the sample size, and that the proposed classifiers have the property of robustness to the margin. The main result of the paper concerns optimal aggregation of classifiers: we suggest a classifier that automatically adapts both to the complexity and to the margin, and attains the optimal fast rates, up to a logarithmic factor.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A2113753">Cited in <strong>7</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A2113753">Cited in <strong>194</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62H30" title="MSC2020">62H30</a> </td> <td class="space"> Classification and discrimination; cluster analysis (statistical aspects) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68T05" title="MSC2020">68T05</a> </td> <td class="space"> Learning and adaptive systems in artificial intelligence </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G99" title="MSC2020">62G99</a> </td> <td class="space"> Nonparametric inference </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aclassification">classification</a>; <a href="/?q=ut%3Astatistical+learning">statistical learning</a>; <a href="/?q=ut%3Aaggregation+of+classifiers">aggregation of classifiers</a>; <a href="/?q=ut%3Aoptimal+rates">optimal rates</a>; <a href="/?q=ut%3Aempirical+processes">empirical processes</a>; <a href="/?q=ut%3Amargins">margins</a>; <a href="/?q=ut%3Acomplexity+of+classes+of+sets">complexity of classes of sets</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1105.62353" data-ciurl="/ci/02113753" data-biburl="/bibtex/02113753.bib" data-amsurl="/amsrefs/02113753.bib" data-xmlurl="/xml/02113753.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/02113753.pdf" title="Zbl 1105.62353 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1214/aos/1079120131" aria-label="DOI for “Optimal aggregation of classifiers in statistical learning.”" title="10.1214/aos/1079120131">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://projecteuclid.org/euclid.aos/1079120131" title="Full Text at Project Euclid">Euclid</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Aizerman, M. 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