Alternating Least Squares Scalar Step

Problem

Take one alternating-least-squares step for a scalar latent factor.

Given user factors U and ratings r, return sum(u_i * r_i) / (sum(u_i ** 2) + lam). An empty input with zero lam returns 0.0.

Hint

This is ridge regression with a single feature, solved in closed form.

case 1

in: [[1,2],[2,4],0]

expected: 2

case 2

in: [[1,2],[2,4],5]

expected: 1

case 3

in: [[1,-1],[3,1],1]

expected: 0.6666666666666666

case 4

in: [[],[],0.5]

expected: 0

Starter codePython

def als_scalar_step(U, r, lam):
    # Your code here
    pass

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