Proximal Algorithms in Statistics and Machine Learning [article]

Nicholas G. Polson, James G. Scott, Brandon T. Willard
<span title="2015-05-30">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form solutions of proximal operators and envelope representations based on the Moreau, Forward-Backward, Douglas-Rachford and Half-Quadratic envelopes. Envelope representations lead to novel proximal algorithms for statistical optimisation of composite objective
more &raquo; ... ons which include both non-smooth and non-convex objectives. We illustrate our methodology with regularized Logistic and Poisson regression and non-convex bridge penalties with a fused lasso norm. We provide a discussion of convergence of non-descent algorithms with acceleration and for non-convex functions. Finally, we provide directions for future research.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="">arXiv:1502.03175v3</a> <a target="_blank" rel="external noopener" href="">fatcat:264vfrtg3rgblpw2ak6vx3ztue</a> </span>
<a target="_blank" rel="noopener" href="" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="" title=" access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> </button> </a>