Logistic Gradient

Compute the gradient of the mean logistic (cross-entropy) loss for a linear model with weights w, evaluated at bias $b=0b=0$. The prediction is $p=\sigma (Xw)p=\backslash sigma(Xw)$ and the labels y are 0/1.

Implement solve(X,y,w).

Returns. Return a tuple (grad_w, grad_b): a NumPy vector with one entry per feature, and a float. Both are averaged over the $nn$ rows.

Examples

Example 1

Input:

solve([[1.0, 2.0], [3.0, 4.0]], [1, 0], [0.0, 0.0])

Output:

([0.5, 0.5], 0.0)

Example 2

Input:

solve([[1.0], [2.0], [3.0]], [0, 1, 1], [0.5])

Output:

([-0.154233], 0.057031)