LASSO Coordinate Step

Problem

Compute one coordinate-descent update for LASSO.

Given the partial residual inner product rho_j and z_j = ||X_j|| ** 2, return soft_threshold(rho_j, lam) / z_j: (rho_j - lam) / z_j when rho_j > lam, (rho_j + lam) / z_j when rho_j < -lam, and 0.0 in between. If z_j is not positive, return 0.0.

Hint

Soft threshold the inner product, then divide by the feature norm squared.

Test cases

case 1

in: [0.5,1,2,0.25]

expected: 0.375

case 2

in: [0.5,0.1,2,0.25]

expected: 0

case 3

in: [0.5,-1,4,0.5]

expected: -0.125

case 4

in: [0.5,0.3,0,0.1]

expected: 0

Starter codePython

def lasso_coordinate_step(x_j, rho_j, z_j, lam):
    # Your code here
    pass

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