Consider a linear-regression model with N=3 and D=1 with input-output pairs as follows:
yl=22, x 1=1, y2=3, x2=1, y3=3, x3=2
What is the gradient of mean-square error (MSE) with respect to B1 (when Bo=0 and B1=1? Give your answer correct to two decimal digits.
MSE Loss = sum((h - y) ** 2) / 2m
Gradient wrt b1 will be sum[(h - y) . x)] / m:
hypothesis: h = b0 + b1.x
for b0 = 0, b1 = 1:
h = x
input(x) : [ 1, 1, 2]
prediction(h) : [ 1, 1, 2]
Ground truth(y) : [ 22, 3, 3]
h - y : [-21, -2, -1]
(h - y). x : [-21, -2, -2]
gradient(b1) : (-21 - 2 - 2) / 3 = -25 / 3 = -8.3333
