Document Zbl 1095.62113

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Inst. Stat. Math.</a> <a href="/?q=in%3A125723" title="Articles in this Issue">58, No. 1, 131-151 (2006)</a>. </div> <div class="abstract">Summary: The estimation of multivariate regression functions from bounded i.i.d. data is considered. The $L_{2}$ error with integration with respect to the design measure is used as an error criterion. The distribution of the design is assumed to be concentrated on a finite set. Neural network estimates are defined by minimizing the empirical $L_{2}$ risk over various sets of feedforward neural networks. Nonasymptotic bounds on the $L_{2}$ error of these estimates are presented. The results imply that neural networks are able to adapt to additive regression functions and to regression functions which are a sum of ridge functions, and hence are able to circumvent the curse of dimensionality in these cases.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5052974">Cited in <strong>5</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62M45" title="MSC2020">62M45</a> </td> <td class="space"> Neural nets and related approaches to inference from stochastic processes </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G08" title="MSC2020">62G08</a> </td> <td class="space"> Nonparametric regression and quantile regression </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ANeural+networks">Neural networks</a>; <a href="/?q=ut%3ADimension+reduction">Dimension reduction</a>; <a href="/?q=ut%3AAdditive+models">Additive models</a>; <a href="/?q=ut%3ACurse+of+dimensionality">Curse of dimensionality</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 1095.62113" data-ciurl="/ci/05052974" data-biburl="/bibtex/05052974.bib" data-amsurl="/amsrefs/05052974.bib" data-xmlurl="/xml/05052974.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05052974.pdf" title="Zbl 1095.62113 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/s10463-005-0005-9" aria-label="DOI for “Nonasymptotic bounds on the $L_{2}$ error of neural network regression estimates”" title="10.1007/s10463-005-0005-9">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">Andrews D.W.K., Whang Y.J. 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