Collaborative Filetering for Christmas Toy Selection. 

The following table shows the ratings on three toys (T1, T2 and
T3)--on a scale of 1 to 3, 3 being the best-- posted by my kid
(Soumya) and four of his friends. For example, Nattie's score on Toy1
is 2 and Chance has not rated Toy 3.

        T1       T2       T3
Natalie  2       3        1
Chance   3       1        -
Sruthi   -       3        3	
Abhishek 2       1        2
Soumya   1       3        -

I.a There is a good sale on Toy 3 over at ToysRThem and I want to see
if I can be cheap as well as a good father. Find Soumya's predicted
score on Toy 3 using the collaborative filtering method explained in
class (In computing the **significance** weight, assume that the weight is
min(1, #items-co-ranked/2).)



Suppose I have done some research and decided that the relevant
features for the toys are: Size and Sound. Size can be "S(mall)" or
"L(arge)". Sound can be "V(ery Noisy)" and "E(xtremely Noisy)". 

I went ahead and classified the three toys

	     Size	    Sound
Toy1          Small	    Very noisy
Toy2	      Large	    Extremely noisy
Toy3	      Small	    Extremely noisy



I.b. Develop a Naive-bayes classifier to do content based prediction
for my son (Soumya). Use it to predict his rating for Toy 3. (In doing this:

  1. assume that any <2 is "Don't Like" and any rating ">= 2" is
     "Like"
  2. do M-estimate correction for the probability--assume that all
     values for attributes are equally likely, and that m is 10. 


I.c. Instead of doing straight content-based prediction, do hybrid
content-based collaborative prediction. Specifically (a) use content
based prediction to fill in Chance and Sruthi's ratings for Toys 3 and
1 (convert "likes" to 2.5 and "don't like" to 1.5)--once again use
M-estimates correction as above. Then use this "filled up" rating
table to predict Soumya's rating for Toy 3. 

Calulators etc allowed, as long as you show your steps. 

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