Lasso Coordinate Descent Sweep

Problem

For a Lasso objective 0.5 * ||A x - b||^2 + lambda * ||x||_1, one coordinate update sets x_j = soft(a_j dot r_j, lambda) / ||a_j||^2, where a_j is column j and r_j = b - sum_{k != j} a_k x_k.

Given A as nested rows, b, x, and lambda, perform one full sweep in order and return the updated x.

Hint

Use the partial residual with all other coordinates fixed.

Test cases

case 1

in: [[[1,0],[0,1]],[1,-2],[0.5,0.5],0.1]

expected: [0.9,-1.9]

case 2

in: [[[1,1]],[2],[1,0],0.5]

expected: [1.5,0]

case 3

in: [[[2,0],[0,2]],[3,4],[0,0],0.25]

expected: [1.4375,1.9375]

Starter codePython

def lasso_coordinate_descent_sweep(a, b, x, lam):
    # Your code here
    pass

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