\documentclass[fleqn]{article}
\usepackage{haldefs}
\usepackage{notes}
\usepackage{url}
\begin{document}
\lecture{Machine Learning}{HW07: Neural modeling and kernels}{CS 726, Fall 2011}
% IF YOU ARE USING THIS .TEX FILE AS A TEMPLATE, PLEASE REPLACE
% "CS 726, Fall 2011" WITH YOUR NAME AND UID.
Hand in at: \url{http://www.cs.utah.edu/~hal/handin.pl?course=cs726}.
Remember that only PDF submissions are accepted. We encourage using
\LaTeX\ to produce your writeups. See \verb+hw00.tex+ for an example
of how to do so. You can make a \verb+.pdf+ out of the \verb+.tex+ by
running ``\verb+pdflatex hw00.tex+''.
\begin{enumerate}
\item Explain how to get a hidden unit to compute an AND function and
then explain how to combine your AND function with the book's OR
function to get XOR. (I.e., define all the weights.)
%\begin{solution}
%\end{solution}
\item Consider Algorithm 27. What would you have to change in order
to do back-propogation of hinge loss and logisitic loss rather than
than squared error?
%\begin{solution}
%\end{solution}
\item Suppose that you have $N$ data points in $D$ dimensions.
Suppose you run perceptron for 1 pass over the data set and it makes
$K$ updates. How long does this take? (Big-O notation, please:
note, it should not actually depend on $K$.) How long would it take
to run if you preprocessed your data with the quadratic feature map?
How long for cubic feature map?
Now, suppose that you run kernelize perceptron over the same data
with a linear kernel. How long will this take (it \emph{should}
depend on $K$ now, and note that under different feature maps, the
numbers $K$ will not be comparable.) What about for quadratic or
cubic kernels?
%\begin{solution}
%\end{solution}
\end{enumerate}
\end{document}