Linear Training Loop

Problem

Train a single-layer linear model with full-batch gradient descent.

x is a list of input vectors and y is a list of target vectors, with W of shape out x in and b of length out. Each epoch computes the mean squared error over all outputs and samples, records it, then updates W and b with gradient descent using learning rate lr. Return [final_W, final_b, losses] where losses has one entry per epoch and is empty when epochs is 0.

Hint

Record the loss before the update so losses[0] reflects the initial parameters.

Test cases

case 1

in: [[[1],[2]],[[3],[5]],[[0]],[0],0.1,2]

expected: [[[1.71]],[1.05],[17,1.685]]

case 2

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

expected: [[[1]],[2],[1]]

case 3

in: [[[1],[2],[3]],[[3],[5],[7]],[[0]],[0],0.05,3]

expected: [[[1.8621481481481483]],[0.8234444444444443],[27.666666666666668,5.488518518518517,1.089693415637859]]

case 4

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

expected: [[[1]],[0.5],[]]

Starter codePython

def train_linear(x, y, W, b, lr, epochs):
    # Return [final_W, final_b, losses]
    # Your code here
    pass

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