Matrix Factorization SGD Update

Problem

Perform one SGD update for matrix factorization.

Given user vector p, item vector q, and observed rating r, compute pred = dot(p, q) and err = r - pred. Return [new_p, new_q] with new_p_i = p_i + lr * (err * q_i - reg * p_i) and new_q_i = q_i + lr * (err * p_i - reg * q_i). Defaults are lr=0.01 and reg=0.02.

Hint

The regularization term pulls each latent vector toward zero every update.

Test cases

case 1

in: [[0.5,0.5],[0.5,0.5],1,0.1,0]

expected: [[0.525,0.525],[0.525,0.525]]

case 2

in: [[1],[2],5,0.1,0]

expected: [[1.6],[2.3]]

case 3

in: [[1],[1],2,0.1,0.1]

expected: [[1.09],[1.09]]

case 4

in: [[0,0],[1,1],3,0.1,0]

expected: [[0.30000000000000004,0.30000000000000004],[1,1]]

Starter codePython

def mf_update(p, q, rating, lr=0.01, reg=0.02):
    # Return [new_p, new_q]
    # Your code here
    pass

4 test cases · run your code against them in the editor