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\begin{document}

\title{Homework 11: Decision Tree and Random Forest}
\author{Prof. Yao Wang}
\date{}

\maketitle

\begin{enumerate}

\item Figure~\ref{fig:p1} shows a partition of the feature space with two features each in the range of 0 to 1. Draw a decision tree that can realize this partition.


\begin{figure}[h]
\centering
\includegraphics[width=0.3\columnwidth]{p1_partition.png}
\caption{The set of samples to be clustered} \label{fig:p1}
\end{figure}
 
  \item\label
Figure~\ref{fig:p2} shows a set of training samples for a binary classification problem. Design a decision tree using the misclassification rate  as the loss function.  Note that given this simple problem, you should be able to ``eyeball'' the correct partition threshold for each possible splitting variable,  instead of using exhaustive search. That is, for each split, consider both features ($x_1$ and $x_2$), but for each feature you should be able to eyeball the proper splitting threshold.

\begin{figure}[h]
\centering
\includegraphics[width=0.3\columnwidth]{p2_classification.png}
\caption{The set of samples to be clustered} \label{fig:p2}
\end{figure}

\end{enumerate}
  \end{document}