\relax 
\@writefile{toc}{\contentsline {section}{\numberline {1}Lagrange Duality}{1}{}\protected@file@percent }
\newlabel{sec:opt_duality}{{1}{1}{}{section.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}The KKT Conditions and the Three Types of Points}{2}{}\protected@file@percent }
\newlabel{sec:opt_kkt}{{2}{2}{}{section.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Deriving the Soft-Margin Dual}{2}{}\protected@file@percent }
\newlabel{sec:opt_soft}{{3}{2}{}{section.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Deriving the SMO Update}{2}{}\protected@file@percent }
\newlabel{sec:opt_smo}{{4}{2}{}{section.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Solving the Dual with a Generic QP Solver}{3}{}\protected@file@percent }
\newlabel{sec:opt_qp}{{5}{3}{}{section.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {6}The Full Platt SMO}{3}{}\protected@file@percent }
\newlabel{sec:opt_platt}{{6}{3}{}{section.6}{}}
\@writefile{toc}{\contentsline {section}{\numberline {7}The SVM as Regularized Loss Minimization (Hinge Loss)}{3}{}\protected@file@percent }
\newlabel{sec:opt_hinge}{{7}{3}{}{section.7}{}}
\newlabel{eq:hingeobj}{{5}{3}{}{equation.5}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Losses as a function of the margin $m=y_if(\mathbf  {x}_i)$. The logistic loss is scaled by $1/\ln 2$ so that it passes through $(0,1)$ like the others.}}{4}{}\protected@file@percent }
\newlabel{fig:losses}{{1}{4}{}{figure.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {8}Support Vector Regression}{5}{}\protected@file@percent }
\newlabel{sec:opt_svr}{{8}{5}{}{section.8}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces SVR on 80 WAVE points (Gaussian kernel, $\sigma =1$, $C=1$). Only points on or outside the tube are support vectors. A wider tube (right) needs fewer support vectors, but the fit is flatter: the peaks are no longer reached.}}{5}{}\protected@file@percent }
\newlabel{fig:svr}{{2}{5}{}{figure.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {9}Historical: VC Dimension and Margins (superseded)}{6}{}\protected@file@percent }
\gdef \@abspage@last{6}