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.
  
  Often 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. 
  
  -----------------------------------------------------------------------------

  Problems for Week 1, due Thursday, September 4

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

  1. Explain, in your own words:
       a) Bayesian approach
       b) Generative model
       c) Discriminative approach

  2. Explain Figure 1.23.

  3. Explain what Equation 1.68 means.

  4. Fill in some steps going from the line before equation 1.41 (defining
     covariance) to equation 1.41. THEN, do exercise 1.6. 

  5. Do exercise 1.11 in the book, and explain in your own words the
     meaning of what you have shown and what the assumptions are. 

DOUBLE VALUE
  6. Consider the problem of finding the "best" line through some points. If you
     ask a software package to do this, what you will typically get is a least
     squares fit based on the deviations in the Y direction of the points from
     the line. 
        a) Explain in more detail the characterization of this "best" line. 

        b) Recognize this as a special case of what is described on
           page 29. Based on the analysis there, give an alternative
           characterization of the "best" line in your own words. What are the
           assumptions (there are at least three that can be mentioned). 

        c) Show that the two characterizations are equivalent, given the
           assumptions. Note that the logic of how to do this is outlined on
           page 29, but you should fill in the gaps to get a better feel for the
           process. 

EXTRA
   7. Exercise 1.27.