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 for
  non-programming assignments 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. For programming assignments, each
  person should turn in their own work. 

  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 11.
  
  Total value is 8. 
  
  Due Thursday. 

  -----------------------------------------------------------------------------


  1. Provide some details to get 4.68.

  2. PRML 4.5. 

  3. Consider the situation in 4.2.1 where the covariances are not the same, but
     there are only two classes. Derive an equation for the decision boundary.
     (As suggested by the text, and figure 4.11, the form of the equation should
     be quadratic). 

  4. The chapter considers several ways to approach the same problem (what is
     it?). Suppose you were the presenter this week, and wanted to make a figure
     or chart that lists the most interesting ones and organizes them in some
     fashion, and notes the similarities, differences, and relationships among
     them. Try your hand at making such a chart or picture.

  QUADRUPLE VALUE
  5. The data files (from assignment three)
         face_train.txt
         no_face_train.txt
         face_test.txt
         no_face_test.txt
     are made from images of faces and non-faces as follows. The images were
     converted to black and white and divided into a 7 by 7 grid, and each block
     was averaged to produce 49 numbers for each image, which are recorded in
     the rows of the above files. 

     This is clearly not a very intelligent way to extract features for face
     detection, but suffices for experimentation. 

     Recall that in assignment three you build a Naive-Bayes classifier from the
     data on the assumption that the conditional densities are Gaussian.

     For this assignment, try using the Fischer Linear Discriminant method to
     project the training data onto a 1D space. Plot a historgram of the
     projected face and non-face data.  Is there a promising cutoff for
     classification? Apply the same transform to the test data, and record how
     well your classifier works.