我无法正确获得此梯度下降解决方案

Question

考虑具有输入输出对的N = 3和D = 1的线性回归模型，如下所示：

yl = 22，x 1 = 1，y2 = 3，x2 = 1，y3 = 3，x3 = 2

当Bo = 0和B1 = 1时，均方误差（MSE）相对于B1的斜率是多少？请正确回答两位小数。

Answer 1

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