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\lecture{Artificial Intelligence}{HW8: Decision Diagrams}{CS5300, Spring 2009}

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% "CS5300, Spring 2009" WITH YOUR NAME AND UID.

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\section{Sampling in the Alarm Network}

Consider the Alarm Network; for instance, slide 2 of day18.

\begin{enumerate}
\item Suppose we ran some sampling algorithm in this domain and
  gathered the following samples:
  \begin{verbatim}
    ~b  ~e  ~a  ~j  ~m
    ~b  ~e   a  ~j  ~m
    ~b  ~e  ~a   j  ~m
    ~b   e   a  ~j   m
    ~b  ~e  ~a  ~j  ~m
     b  ~e  ~a  ~j   m
    ~b   e   a   j  ~m
    ~b  ~e   a   j   m
  \end{verbatim}
  Please estimate the following quantities based on these sample:
  \begin{enumerate}
    \item $p(b)$
    \item $p(b \| a)$
    \item $p(j \| b)$
    \item $p(e \| b, \lnot a)$
  \end{enumerate}
\item Do you think these samples are actually samples from the alarm
  network's probability distribution?  Why or why not?
\item Suppose that we had the following samples with \emph{likelihood
    weights}.  Estimate the same quantities as before:
  \begin{verbatim}
    ~b  ~e  ~a  ~j  ~m            1.3
    ~b  ~e   a  ~j  ~m            2.3
    ~b  ~e  ~a   j  ~m            0.2
     b  ~e  ~a  ~j   m            1.1
    ~b   e  ~a  ~j  ~m            0.5
     b  ~e  ~a   j  ~m            1.2
    ~b   e   a   j  ~m            5
    ~b  ~e   a   j   m            0.01
  \end{verbatim}
  Please estimate the following quantities based on these sample:
  \begin{enumerate}
    \item $p(b)$
    \item $p(b \| a)$
    \item $p(j \| b)$
    \item $p(e \| b, \lnot a)$
  \end{enumerate}
\item Suppose I wanted to estimate $p(m \| b)$.  Would prior sampling
  work well in this case (why or why not)?  What about rejection
  sampling?  How many samples do you think you'd need to draw (order
  of magnitude) to get reasonable estimates for these two approaches?
\end{enumerate}

\section{Decisions in Class}

Alice is back, and still trying to pass evil Clarence's class.  This
time she wants to model the class as a Bayes net.  As before, there
are two decisions she has to make.  First, whether to study or not.
Second, whether to sweet-talk Clarence or not.  If she studies, she
learns the material with probability $0.9$.  If she does not study,
she learns the material with probability $0.01$ (luck).  If she
sweet-talks Clarence, he ends up in a good mood with probability
$0.7$; if she does not, he is in a good mood with probability $0.5$.
Her final grade (whether she passes or not) depends on whether she
learns the material \emph{and} whether Clarence is in a good mood.  If
they're both true, she passes with probability $0.99$.  If she learns
the material but Clarence is in a bad mood, she passes with
probability $0.8$.  If she doesn't learn the material, but Clarence is
in a good mood, she passes with probability $0.5$.  If she doesn't
learns the material and Clarence is in a bad mood, she passes with
probability $0.1$.

\begin{enumerate}
\item Represent this situation as a Bayes net, complete with CPTs and
  decision nodes (appropriately shaped).

\item What is the value of information for knowing Clarence's mood?


\item (Extra credit for everyone!) Download the samiam program from
  Adnan Darwiche's website (at UCLA) and implement this in that set up
  (it's pretty easy).  You probably will need to make the decision
  nodes just standard nodes.  Do inference for all four possible
  action choices that Alice can make: what are the probabilities of
  passing for each.  Please include a screenshot of the network in
  query mode.
\end{enumerate}


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