Sue want to build a model to predict

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Sue want to build a model to predict movie ratings. She has a matrix of data, where for M movies and U users she has collected ratings between 1 and 5. Not all users have rated all movies. These entries are indicated by a “? ”. Sue has build a model that can predict unrated movies for any user u in the database. The model always predicts a real number, q, between 1 and 5. To further optimize her predictions she decides to train another model that maps her predictions q to new rating estimates q’. To train this model she uses all observed ratings in the database (i. e. ignoring “? ”) and fits a neural network as follows: Here “i” runs over all observed ratings, and |. | denotes the absolute value. 1) Derive the gradients 2) Give pseudo-code for a stochastic gradient descent algorithm for learning “a” and “b”. 3) Given a fixed step-size, explain if this algorithm will converge after infinitely many gradient updates? 4) Jimmy has another algorithm that also predicts ratings. Sue and Jimmy decide to combine their models and compute a bagged estimate. Calling Sue prediction q_sue and Jimmy prediction q_jim give an expression for a combined prediction using bagging. 5) Explain whether bagging increases or decreases variance and why.