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  Problems for Week 9.
  
  Total value is 6, with 2 extra available, but the extra problem needs to be
  handed in by class Tuesday to get the 2 extra points.
  
  Due Thursday, but since I was slow in posting the assignment, I will accept
  late submissions.

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  EXTRA, value is 2, but must be handed in by 3:00 Tuesday to count for grades.
  Especially recomended for those weak on participation grades. If you choose
  not to do this for grades, please take 20 minutes to jot down some thoughts
  to help improve discussion. 

  1. Put on your philosopher's hat, and/or take a step back from the course so
     far and write about a page explaining what, in your own mind, is the point
     of it all. If you think that there is not much point, feel free to argue
     that, but you will need to understand the other side well enough to argue
     against it.  Your essay should be usable as a document that convinces
     others to study the subject. Your essay might address points such as:

     a). Why probabilistic methods are so important.

     b). What is a statistical model, and what are some of the advantageous of
         thinking about data from this perspective.
         
     c). Why relatively simple models might be able to succeed, despite the
         potentially very large complexity of data. 

  2. (Value is 6). 

  Read one or more of the following papers (the first pair counts as one), and
  write either a one page summary for two of them, or a more thoughtful two page
  summary of one of them. Your summary should address the papers in the context
  of what you have learned in the course.

  Dimensionality reduction by projection onto non-linear manifolds (two papers,
  counts as one):
     Paper one.
     Paper two.

  An application to graphics.

  Applications to computer vision

  Application to learning the semantics of images.