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. 
  
  -----------------------------------------------------------------------------

  Problems for Week 3, due Thursday, Feb 1. 
  
  Total value is 8.

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

  1. Problem 8.3

  2. Problem 8.6 

  3. Problem 8.10 

  4. Problem 8.13

  QUADRUPLE VALUE
  5. The data files 
         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. 

     Build a Naive-Bayes classifier from the data on the assumption that the
     conditional densities are Gaussian. Write a few sentences about what you
     did, and what your accuracy was on the training and test data sets.
     Further, comment on some of the assumptions this classifier relies on.
     
     For the record, submit your program that computes the answer, but the
     graders won't necessarily look at it unless something your writeup suggests
     that they should. Hence you can use any programming language that you like.
     Again, if you have no opinion, I suggest using Matlab. If you want to try
     Matlab, but have no prior experience, then you will have to spend some time
     getting familiar with it, which is likely time well spent.  Some
     information about getting started is 
          linked here.