\item \subquestionpoints{10} \textbf{Coding problem}

Consider a website that wants to predict its
daily traffic. The website owners have collected a dataset of past traffic to
their website, along with some features which they think are useful in
predicting the number of visitors per day. The dataset is split into
train/valid sets and the starter code is provided in the following files:
\begin{center}
\begin{itemize}
\item 	\url{src/poisson/{train,valid}.csv}
\item   \url{src/poisson/poisson.py}
\end{itemize}
\end{center}
We will apply Poisson regression to model the number of visitors per day.
Note that applying Poisson regression in particular assumes that the data
follows a Poisson distribution whose natural parameter is a linear
combination of the input features (\emph{i.e.,} $\eta = \theta^T x$).
In \texttt{src/poisson/poisson.py}, implement Poisson regression for this dataset
and use \emph{full batch gradient ascent} to maximize the log-likelihood of $\theta$. For the
stopping criterion, check if the change in parameters has a norm smaller than
a small value such as $10^{-5}$.

Using the trained model, predict the expected counts for the \textbf{validation set}, and
create a scatter plot between the true counts vs predicted counts (on the
validation set). In the scatter plot, let x-axis be the true count and y-axis
be the corresponding predicted expected count. Note that the true counts
are integers while the expected counts are generally real values.