Could you help giving me explanation on this problem about Polynomial Regression(Machine learning)?

Data are independently generated from the following random variable

Y=cos(2?X)+?,

whereX?Uniform([0,1]) and??N(0,?2) are independent.

I chose sigma = 0.4 and 1.

I choose N =100 as data size.

I chose degree of freedom 9.

The figure of Maximum Likelihood :

std of noise = 0.40 std of noise = 1.00 3 1.0 2 0.5 0.0 0 -1 -0.5 -2 train data . train data -1.0 y = true poly -3 y = true poly y = predicted mean y = predicted mean 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0std of noise = 0.40 std of noise = 1.00 1.5 1.0 2 0.5 0 0.0 -1 -0.5 -2 train data . -1.0 train data y = true poly -3 y = true poly + y = predicted mean + y = predicted mean 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0