This week we are experimenting with a different format. No summaries are
  required for this week, but the first half of the problems are due on Tuesday.
  This is simply to ensure that everyone is ready for the discussion.
  

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  Unless otherwise specified, questions have unit value. The total value of the
  assignments from each week will vary substantively.
  
  Recall that assignments are graded rather loosely on effort, and that 3/4 of
  the total marks (1/2 for ugrads) over all assignments over all weeks
  represents 100%. This policy is in place partly to allow for error in the
  grading approach which, by necessity, is somewhat subjective, and needs to be
  done somewhat superficially. It is recommended (and requested) that you try to
  overshoot the 3/4 requirement, rather than worry about the details of how the
  grading is done. 

  Problems denoted EXTRA can be substituted for other problems, or done in
  addition, but they do not count towards the computation of the 3/4
  requirement. They may be discussed in class depending on time and interest.
  They are problems that I think might be useful, and likely be assigned if we
  had more time per chapter.
  
  Sometimes you will explicitly have to choose some of your own problems. Even
  when this is not the case, you can substitute some problems in the book if
  they appear more helpful to you. For now, limit the number of substitutions to
  50% of what you hand in. This parameter may be increased or decreased as we go
  on.  
  
  You are encouraged to discuss the problems with your peers, but I would like
  individual final submissions demonstrating effort and understanding of what
  was done. If you end up working closely with someone on a problem set, make a
  note on your submission saying who it was. 

  Since this is graduate level research course that is graded predominately on
  effort, I am confident that there will not be any problems with academic
  honesty. However, do note that non-negligible deviations are often
  surprisingly easy to spot, and can be verified by discussing the submitted
  solutions with the student. 
  
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  Problems for Week 4. 
  
  Total value is 7. 
  
  First 3/7 are due Tuesday, second 4/7 Thursday. To hand in extra work on
  Thursday, simply resubmit an updated document via turnin.

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  1. Write a paragraph identifying the main underlying points of the chapter.
     You likely want take the chapter as a whole (i.e., including last week's
     reading, but give the second part (this week's reading) at least equal
     consideration. 

  2. To quote the author on page 396: "The reader is encouraged to study this
     reorganization carefully ...". Do this by filling in the "reorganization"
     steps to derive 8.52. If you are having trouble with this, start with a
     small number of nodes (perhaps 5, two on each side of the node that is
     being marginalized. 

  3. a) Explain why a standard directed tree is moral. 
     b) Is the graph in Figure 8.2 moral? If not, make it moral (and undirected). 
     c) What are the potential functions associated with each clique that make
        up the factorization?
     d) Draw an immoral graph with at least nine nodes, and deal with its morality
        problems (e.g. make it moral and undirected). 
     e) Provide a factor graph for Figure 8.2. 

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  The following problems can be done for Thursday. Overwrite your submission
  with an updated one with any extra problems included. 
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  4. Provide some of the details to get 8.63.

  5. Referring to the example on page 409, explain the sum-product algorithm. 
     Be sure to say what is being computed, and what needs to be stored. 

  6. Book, number 8.27

  7. a) What does the max-sum algorithm compute? 
     b) What does the modified version compute (page 414). 
     c) Why is the modification necessary?