Question 6 (Matrix Factorization (7 pts)) Consider the following modified Matrix Factorization (MF) model where we made

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Question 6 Matrix Factorization 7 Pts Consider The Following Modified Matrix Factorization Mf Model Where We Made 1 (142.3 KiB) Viewed 39 times

Question 6 (Matrix Factorization (7 pts)) Consider the following modified Matrix Factorization (MF) model where we made two changes to the basic MF model. First, we introduced a bias for each user, b; for ith user, and also used li regularization to regularize the latent features of users instead of l2 norm. The modified objective became as follows: m min b1,b2,...,bn (Rij – (u, v; +b;))? + a + || 17||1 +B || 03/13, i=1 j=1 U1,..., Un ERK (,j) en V1,...,Um ERK where N is the subset of observed ratings, n is the number of users, m is the number of movies, K is the number of latent features to be extracted, and ui, i = 1, 2, ..., n and vj, j = 1, 2, ..., m are the latent features for users and movies, respectively. a) Write the closed form solution for the bias of ith user bi assuming everything else is fixed. b) Write out the Stochastic Gradient Update for u; at iteration t (not the full SGD algorithm, just the update rule)