Poisson Regression IRLS Step

Problem

Run one IRLS step for Poisson regression with a log link.

For each observation compute mu_i = exp(w * x_i), working response z_i = w * x_i + (y_i - mu_i) / mu_i, and weight W_i = mu_i. Return sum(W_i * x_i * z_i) / sum(W_i * x_i ** 2), or w when the denominator is zero.

Hint

For a log link the IRLS weights equal the Poisson means.

Test cases

case 1

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

expected: 0.4

case 2

in: [0.5,[1,2],[1,3]]

expected: 0.49318911045422326

case 3

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

expected: 0.7182818284590451

Starter codePython

def poisson_irls_step(w, X, y):
    # Your code here
    pass

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