Document Zbl 1550.62016

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Comput.</a> <a href="/?q=in%3A520975" title="Articles in this Issue">34, No. 6, Paper No. 188, 19 p. (2024)</a>. </div> <div class="abstract">Summary: Support vector machine (SVM) is a powerful binary classification tool, but the growing size of modern data is bringing challenges to it. First, the non-smoothness of hinge loss poses difficulties in large-scale computation. Second, the existing large-scale distributed algorithms heavily rely on uniformity and randomness conditions, which are frequently violated in practice. To solve these issues, we first construct a convolution smoothing SVM, which enjoys a smooth and convex objective function. Then a distributed SVM is developed, in which the estimator can be calculated conveniently by minimizing a pilot sample-based distributed surrogate loss. In particular, it can be adaptive when the uniformity or randomness condition is violated. The established theoretical results and numerical experiments on both synthetic and real data all confirm the proposed methods.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62-08" title="MSC2020">62-08</a> </td> <td class="space"> Computational methods for problems pertaining to statistics </td> </tr><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%3A62R07" title="MSC2020">62R07</a> </td> <td class="space"> Statistical aspects of big data and data science </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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Alinear+support+vector+machine">linear support vector machine</a>; <a href="/?q=ut%3Aconvolution+smoothing">convolution smoothing</a>; <a href="/?q=ut%3ABahadur+representation">Bahadur representation</a>; <a href="/?q=ut%3Adistributed+algorithm">distributed algorithm</a></div> <div class="software"> <h3>Software:</h3><a href="/software/4880">LIBLINEAR</a>; <a href="/software/12678">SSVM</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 1550.62016" data-ciurl="/ci/07949293" data-biburl="/bibtex/07949293.bib" data-amsurl="/amsrefs/07949293.bib" data-xmlurl="/xml/07949293.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07949293.pdf" title="Zbl 1550.62016 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/10.1007/s11222-024-10506-5" aria-label="DOI for “Support vector machine in big data: smoothing strategy and adaptive distributed inference”" title="10.1007/s11222-024-10506-5">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Blanchard, G.; Bousquet, O.; Massart, P., Statistical performance of support vector machines, Ann. 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