\documentclass[12pt]{article}
\usepackage{geometry}                % See geometry.pdf to learn the layout options. There are lots.
\geometry{letterpaper}                   % ... or a4paper or a5paper or ... 
%\geometry{landscape}                % Activate for for rotated page geometry
\usepackage[parfill]{parskip}    % Activate to begin paragraphs with an empty line rather than an indent
\usepackage{daves,fancyhdr,natbib,graphicx,dcolumn,amsmath,lastpage,url}
\usepackage{amsmath,amssymb,epstopdf,longtable}
\usepackage[final]{pdfpages}
\DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `dirname #1`/`basename #1 .tif`.png}
\pagestyle{fancy}
\lhead{CE 5319 Machine Learning for Civil Engineers}
\rhead{SUMMER 2025}
\lfoot{ES8}
\cfoot{}
\rfoot{Page \thepage\ of \pageref{LastPage}}
\renewcommand\headrulewidth{0pt}



\begin{document}
\begin{center}
{\textbf{{ CE 5319 Machine Learning for Civil Engineers} \\ {Exercise Set 8} \\ {Feature Reduction and Distance Metric in KNN Regression} }}
\end{center}

\section*{\small{Exercises}}
\begin{enumerate}
\item Using the implementation of \texttt{KNeighborsRegressor} on the \texttt{Solids\_in\_Rivers} database, complete the following tasks:\footnote{This exercise is to develop intuition around (a) which features matter most in KNN regression and (b) how the choice of distance metric can influence model behavior.}

\begin{enumerate}
    \item Use the \texttt{permutation\_importance} function from \texttt{sklearn.inspection} to estimate the importance of each feature in your dataset.
    \item Identify the top 5 or 6 most important features based on the permutation importance scores.
    \item Retrain the \texttt{KNeighborsRegressor} model using only the reduced feature set. Keep the same number of neighbors as in your full model.
    \item Compare the performance of the reduced model to the full model using at least the following metrics:
    \begin{itemize}
        \item Coefficient of determination ($R^2$ score)
        \item Root mean square error (RMSE)
    \end{itemize}
    \item For a fixed input vector (you may use the one from the earlier example), show the estimate computed using both models (full and reduced). Are they close? Provide a short explanation.
    \item Repeat the modeling using two different distance powers: $p=1$ (Manhattan) and $p=2$ (Euclidean). Comment on how the distance metric affects:
    \begin{itemize}
        \item Feature importance rankings
        \item Estimated values
        \item Model performance
    \end{itemize}
\end{enumerate}




\end{enumerate}


\end{document}