Gradient Descent Step

Problem

Perform one gradient descent step for linear regression with intercept. With predictions pred_i = w0 + w1*x_i and residuals r_i = pred_i - y_i, the gradients are (2/n)*sum(r_i) for w0 and (2/n)*sum(r_i*x_i) for w1.

Return [w0 - lr*grad0, w1 - lr*grad1]; empty X returns [w0, w1].

Hint

Compute residuals once, then use them for both the intercept and slope gradients.

Test cases

case 1

in: [[1,2,3],[2,4,6],0,0,0.1]

expected: [0.8,1.8666666666666665]

case 2

in: [[1,2,3],[2,4,6],1,2,0.1]

expected: [0.8,1.6]

case 3

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

expected: [1,0]

case 4

in: [[],[],3,4,0.1]

expected: [3,4]

Starter codePython

def gd_step_linear(X, y, w0, w1, lr):
    # Returns [new_w0, new_w1]
    # Your code here
    pass

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