\documentclass{article}
\input{mathmacro}
\usepackage{amsmath}
\begin{document}

\section{Q1}
\subsection{1 (7 points)}
\begin{itemize}
\item[+7] if numbers are right
\end{itemize}

\subsection{2 (23 points)}
\begin{itemize}
\item[+7] plot looks correct (circles tend towards the boundary)
\item[+5] say that thre error is a random variable
\item[+6] errors of AC are reasonable, and train > test
\item[+6] mention that AC points tend to be chosen around boundary
\item[+3] mention that low-density points help little (and/or that
reducing the grid bounds would help)
\item[+3] mention other thoughts that appear in the solutions 
\end{itemize}

\pagebreak
\section{Q2}
\subsection{1 (25 points)}
\begin{itemize}
\item[+7] use the hint i.e. write
\begin{equation}\label{eq1}
\Ep{p(x,y)}{L(y,\hat{y}(x))}=\ldots = \int_xp(x)\sum_y\left(1-\delta_{y,\hat{y}(x)}\right)p(y|x)dx
\end{equation}
(+ 3 if start right but then get confused)
\item[+8] show (convincingly)  it is enough to minimize cost for
every $x$
\item[+4] only say it is enough to minimize for every $x$ (not
convincing they understand why it's enough)
\item[+10] derive thre rule from \eqref{eq1} 
\end{itemize}

\subsection{2 (10 points)}
\begin{itemize}
\item[+6] correct rule (in general form)
\item[+4] explain how to derive
\item[+2] show simplification for binary case
\end{itemize}
do not deduct points fro same mistakes as in 1!


\pagebreak
\section{Q3}
\subsection{1 (10 points)}
\begin{itemize}
\item[+2] right numbers
\item[+2] right plots
\item[+4] say that as $n\to\infty$ boundar approaches the optimal
boundary
\item[+2] only say that boundary becomes linear (without saying that
optimal boundary is linear)
\item[+2] explain it is difficult to estimate Gaussians with few
points
\item[-2] say the boundary for \texttt{XYlarge} \textbf{is} linear
\end{itemize}

\subsection{2 (25 points)}
\begin{itemize}
\item[+2] right numbers 
\item[+2] right plots
\item[+3] say that the two models have similar generalization
error when trained on \texttt{XYlarge}.
\item[+5] explain disatvantage of generative models with few points
(diificult to estimate Gaussians)
\item[+15] explain that boundaries approach each other, and the optimal
boundary

(only +7 if claims are correct but not explained)
\item[+7] only say boundaries both approach a linear boundary (but do
not say that's the optimal boundary)
\item[-5] say one of the methods (or both) can not produce linear
boundary (or have different number of degrees of freedom)
\item[-3] say log. reg. is much worse because the boundary looks worse
\end{itemize}
\end{document}
