Suppose you run a bookstore, and have ratings (1 to 5 stars) of books. Your collaborative filtering algorithm has learned a parameter vector for user j, and a feature vector 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=1∑nuj=1r(i, j)). [Hint: Two of the four options below are correct.]
a) 1m∑(i, j):r(i, j)=1((θ(j))Tx(i)−r(i, j))2
b) 1m∑nmi=1∑j:r(i, j)=1(∑nk=1(θ(j))kx(i)k−y(i, j))2
c) 1m∑(i, j):r(i, j)=1((θ(j))Tx(i)−y(i, j))2
d) 1m∑nuj=1∑i:r(i, j)=1(∑nk=1(θ(k))jx(k)i−y(i, j))2