Suppose you run a bookstore, and have ratings (1 to 5 stars)

of books. Your collaborative filtering algorithm has learned

a parameter vector (j) for user j, and a feature

vector x(i) for each book. You would like to compute the

"training error", meaning the average squared error of your

system's predictions on all the ratings that you have gotten

from your users. Which of these are correct ways of doing so (check all that apply)?

For this problem, let m be the total number of ratings you

have gotten from your users. (Another way of saying this is

that m=nmi=1nuj=1r(i,j)). [Hint: Two of the four options below are correct.]

1m(i,j):r(i,j)=1(((j))Tx(i)r(i,j))2

1mnmi=1j:r(i,j)=1(nk=1((j))kx(i)ky(i,j))2

1m(i,j):r(i,j)=1(((j))Tx(i)y(i,j))2

1mnuj=1i:r(i,j)=1(nk=1((k))jx(k)iy(i,j))2