\relax \@writefile{toc}{\contentsline {section}{\numberline {1}Setup and Notation}{1}{}\protected@file@percent } \newlabel{sec:setup}{{1}{1}{}{section.1}{}} \newlabel{eq:predictor}{{1}{1}{}{equation.1}{}} \@writefile{toc}{\contentsline {section}{\numberline {2}Cost Function: Least Squares}{2}{}\protected@file@percent } \newlabel{eq:sse}{{2}{2}{}{equation.2}{}} \@writefile{toc}{\contentsline {section}{\numberline {3}A First Closed-Form Solution: One Feature, by Hand}{2}{}\protected@file@percent } \newlabel{sec:1d}{{3}{2}{}{section.3}{}} \newlabel{eq:1d-a}{{3}{2}{}{equation.3}{}} \newlabel{eq:1d-b}{{4}{2}{}{equation.4}{}} \newlabel{eq:1d-solution}{{5}{2}{}{equation.5}{}} \@writefile{toc}{\contentsline {section}{\numberline {4}Least Squares via Normal Equations}{3}{}\protected@file@percent } \newlabel{sec:normaleq}{{4}{3}{}{section.4}{}} \newlabel{eq:normaleq}{{6}{3}{}{equation.6}{}} \@writefile{toc}{\contentsline {section}{\numberline {5}Overfitting and the Need to Regularize}{3}{}\protected@file@percent } \newlabel{sec:overfit}{{5}{3}{}{section.5}{}} \@writefile{toc}{\contentsline {section}{\numberline {6}Ridge Regression}{4}{}\protected@file@percent } \newlabel{sec:ridge}{{6}{4}{}{section.6}{}} \newlabel{eq:ridge-primal}{{7}{4}{}{equation.7}{}} \newlabel{eq:ridge-lagrangian}{{8}{5}{}{equation.8}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Solving Ridge: Why the Intercept Needs Special Care}{5}{}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Ridge Closed Form (same ``quick'' style as \S \ref {sec:normaleq})}{6}{}\protected@file@percent } \newlabel{eq:ridge-closedform}{{9}{6}{}{equation.9}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.3}Worked Example, Continued}{6}{}\protected@file@percent } \newlabel{sec:ridge-solution}{{6.3}{6}{}{subsection.6.3}{}} \@writefile{toc}{\contentsline {section}{\numberline {7}Generalizing: $L_q$ Regularizers and Lasso}{7}{}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {8}Implementation Notes (HW1)}{7}{}\protected@file@percent } \newlabel{sec:implementation}{{8}{7}{}{section.8}{}} \@writefile{toc}{\contentsline {section}{\numberline {9}Gradient Descent: A General Iterative Optimizer}{8}{}\protected@file@percent } \newlabel{sec:gd}{{9}{8}{}{section.9}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {9.1}Minimizing a Function}{8}{}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {9.2}The Gradient Vector and the Algorithm}{9}{}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {9.3}Gradient Descent for Linear Regression --- a Worked Sandbox}{10}{}\protected@file@percent } \newlabel{eq:gd-update}{{10}{10}{}{equation.10}{}} \@writefile{toc}{\contentsline {section}{\numberline {10}Next Module: From Regression to Classification}{11}{}\protected@file@percent } \gdef \@abspage@last{11}